Ph v«  •! 


£=mutl)s3oman:  jHtecellaneoujs  Collection?! 

1O38 


.  SMITHSONIAN 


PHYSICAL  TABLES 


PREPARED  BY 

THOMAS    GRAY 

FOURTH  REVISED  EDITION 


CITY   OF   WASHINGTON 

PUBLISHED    BY   THE   SMITHSONIAN   INSTITUTION 

1908 


f 

PRESvS    WORK   BY   JUDD    &   DETWEH^R,    INC., 
WASHINGTON,   D.  C. 


ADVERTISEMENT   TO    REVISED    EDITION. 


THE  edition  of  the  Smithsonian  Physical  Tables  issued  in  1896  having 
become  exhausted,  a  careful  reexamination  of  the  original  work  has  been  made 
at  my  request  by  the  author,  Professor  Gray,  and  the  few  changes  found  neces- 
sary have  been  made  in  the  plates. 

S.  P.  LANGLEY, 

Secretary. 

SMITHSONIAN  INSTITUTION, 
WASHINGTON  CITY,   October  30,  1897* 


ADVERTISEMENT   TO   SECOND    REVISED    EDITION. 


THE  revised  edition  of  the  Smithsonian  Physical  Tables  issued  in  1897 
having  become  exhausted,  and  the  demand  continuing,  a  second  revised 
edition  is  now  issued.  The  author,  Professor  Gray,  has  again  examined  the 
work  and  made  a  few  corrections  in  the  plates,  table  283  in  particular  being 
rewritten  to  agree  with  the  recent  report  of  the  International  Committee  on 
Atomic  Weights. 

S.  P.  LANG  LEY, 

Secretary. 

SMITHSONIAN  INSTITUTION, 
WASHINGTON  CITY,   January,  igoj. 


ADVERTISEMENT  TO  THIRD  REVISED  EDITION. 


The  second  revised  edition  of  the  Smithsonian  Physical  Tables  issued  in 
January,  1903,  having  become  exhausted,  and  the  demand  for  the  work 
continuing,  a  third  revised  edition  is  now  published,  \\\  which  the  author 
has  made  a  few  corrections  to  agree  with  the  latest  researches. 

S.  P.  LANGLEY, 

Secretary. 

SMITHSONIAN  INSTITUTION,  .  f  |RA  A 

WASHINGTON  CITY    April,  1904. 


ADVERTISEMENT  TO  FOURTH   REVISED  EDITION. 


The  third  revised  edition  of  the  Smithsonian  Physical  Tables  issued  in 
190}  having  become  exhausted,  a  fourth  revised  edition  is  now  published,  in 
which  the  author,  Professor  Gray,  has  made  a  few  corrections,  particularly 
in  the  tables  of  equivalents  of  metric  and  British  Imperial  weights  and  meas- 
ures, which  are  here  brought  up  to  date.  The  other  changes  from  the  third 
edition  are  in  Table  36,  page  27,  2. 3349  x  io~2  for  2.3349  ;  Table  100,  page 
89,  coal  gas,  0.320  for  0.340,  0.740  for  0.450,  0.000414  for  0.000421,  0.000957 
for  0.000558,  0.02583  for  0.02628,  and  0.05973  for  0.03483  ;  Table  102,  page 
92,  Temperature  20°,  2 126  for  4126  ;  Table  104,  page  94,  Temperature  46°  lo 
95°,  1.01014,  etc.,  for  1.00014,  etc->  and  100°,  1.02312  for  1.00312;  foot- 
note to  Table  133,  page  120,  /',  and  a  (/'  —  /)  the  correction  for  temperature, 
for  t'  and  at  the  correction  for  temperature  ;  Table  174,  page  162,  .0118421 
for  .0184210;  Table  175,  page  162,  .16058  for  .16858  ;  Table  227,  page  220, 
414  X  io5  ergs  per  gramme  degree  for  414.0  ergs  per  gramme  degree  ;  Table 
268,  page  258,  Less  than  T^7  for  Less  than  T^. 

CHAS.  D.  WAIXOTT, 

Secretary. 
SMITHSONIAN  INSTITUTION, 

WASHINGTON  CITV,  June,  1908. 


ADVERTISEMENT. 


IN  connection  with  the  system  of  meteorological  observations  established  by 
the  Smithsonian  Institution  about  1850,  a  series  of  meteorological  tables  was 
compiled  by  Dr.  Arnold  Guyot,  at  the  request  of  Secretary  Henry,  and  was  pub- 
lished in  1852.  A  second  edition  was  issued  in  1857,  and  a  third  edition,  with 
further  amendments,  in  1859.  Though  primarily  designed  for  meteorological 
observers  reporting  to  the  Smithsonian  Institution,  the  tables  were  so  widely 
used  by  physicists  that,  after  twenty-five  years  of  valuable  service,  the  work  was 
again  revised  and  a  fourth  edition  was  published  in  1884.  In  a  few  years  the 
demand  for  the  tables  exhausted  the  edition,  and  it  appeared  to  me  desirable  to 
recast  the  work  entirely,  rather  than  to  undertake  its  revision  again.  After  care- 
ful consideration  I  decided  to  publish  a  new  work  in  three  parts  —  Meteorologi- 
cal Tables,  Geographical  Tables,  and  Physical  Tables  —  each  representative  of 
the  latest  knowledge  in  its  field,  and  independent  of  the  others,  but  the  three 
forming  a  homogeneous  series.  Although  thus  historically  related  to  Dr.  Guyot's 
Tables,  the  present  work  is  so  entirely  changed  with  respect  to  material,  arrange- 
ment, and  presentation  that  it  is  not  a  fifth  edition  of  the  older  tables,  but  essen- 
tially a  new  publication. 

The  first  volume  of  the  new  series  of  Smithsonian  Tables  (the  Meteorological 
Tables)  appeared  in  1893,  and  so  great  has  been  the  demand  for  it  that  a  second 
edition  has  already  become  necessary.  The  second  volume  of  the  series  (the 
Geographical  Tables),  prepared  by  Prof.  R.  S.  Woodward,  was  published  in  1894. 
The  present  volume  (the  Physical  Tables),  forming  the  third  of  the  series,  has 
been  prepared  by  Prof.  Thomas  Gray,  of  the  Rose  Polytechnic  Institute,  Terre 
Haute,  Indiana,  who  has  given  to  the  work  the  results  of  a  wide  experience. 

S.  P.  LANGLEY,  Secretary. 


PREFACE. 


IN  the  space  assigned  to  this  book  it  was  impossible  to  include,  even  approxi- 
mately, all  the  physical  data  available.  The  object  has  been  to  make  the  tables 
easy  of  reference  and  to  contain  the  data  most  frequently  required.  In  the 
subjects  included  it  has  been  necessary  in  many  cases  to  make  brief  selections 
from  a  large  number  of  more  or  less  discordant  results  obtained  by  differ- 
ent experimenters.  I  have  endeavored,  as  far  as  possible,  to  compile  the  tables 
- 

from  papers  which  are  vouched  for  by  well-known  authorities,  or  which,  from 
the  method  of  experiment  and  the  apparent  care  taken  in  the  investigation,  seem 
likely  to  give  reliable  results. 

Such  matter  as  is  commonly  found  in  books  of  mathematical  tables  has  not 
been  included,  as  it  seemed  better  to  utilize  the  space  for  physical  data.  Some 
tables  of  a  mathematical  character  which  are  useful  to  the  physicist,  and  which 
are  less  easily  found,  have  been  given.  Many  of  these  have  been  calculated  for 
this  book,  and  where  they  have  not  been  so  calculated  their  source  is  given. 

The  authorities  from  which  the  physical  data  have  been  derived  are  quoted  on 
the  same  page  with  the  table,  and  this  is  the  case  also  with  regard  to  explanations 
of  the  meaning  or  use  of  the  tabular  numbers.  In  many  cases  the  actual  numbers 
given  in  the  tables  are  not  to  be  found  in  the  memoirs  quoted.  In  such  cases 
the  tabular  numbers  have  been  obtained  by  interpolation  or  calculation  from  the 
published  results.  The  reason  for  this  is  the  desirability  of  uniform  change  of 
argument  in  the  tables,  in  order  to  save  space  and  to  facilitate  comparison  of 
results.  Where  it  seemed  desirable  the  tables  contain  values  both  in  metric  and 
in  British  units,  but  as  a  rule  the  centimetre,  gramme,  and  second  have  been  used 
as  fundamental  units.  In  the  comparison  of  British  and  metric  units,  and  quan- 
tities expressed  in  them,  the  metre  has  been  taken  as  equal  to  39.37  inches, 
which  is  the  legal  ratio  in  the  United  States.  It  is  hardly  possible  that  a  series 


IV  PREFACE. 

, 

of  tables,  such  as  those  here  given,  involving  so  much  transcribing,  interpolation, 
and  calculation,  can  be  free  from  errors,  but  it  is  hoped  that  these  are  not  so 
numerous  as  to  seriously  detract  from  the  use  of  the  book. 

I  wish  to  acknowledge  much  active  assistance  and  many  valuable  suggestions 
during  the  preparation  of  the  book  from  Professors  S.  P.  Langley,  Carl  Barus, 
F.  W.  Clarke,  C.  L.  Mees,  W.  A.  Noyes,  and  Mr.  R.  E.  Huthsteiner.  I  am  also 
under  obligations  to  Professors  Landolt  and  Bernstein,  who  kindly  placed  an 
early  copy  of  their  "  Physikalisch-Chemische  Tabellen  "  at  my  disposal. 

THOMAS  GRAY. 

ROSE  POLYTECHNIC  INSTITUTE, 

TERRE  HAUTE,  IND.,  July  13,  1896. 


TABLE    OF    CONTENTS. 


PAGB 

Introduction  on  units  of  measurement  and  conversion  factors xv 

Units  of  measurement,  general  discussion xv 

Dimension  formulae  for  dynamic  units xvii 

"   heat  units xxiii 

"  of  electric  and  magnetic  units,  general  discussion xxv 

formulae  in  electrostatic  system xxvi 

"  electromagnetic  system xxix 

Practical  units  of  electricity,  legalization  of xxxiii 

• 

TABLE 

1.  Formulae  for  conversion  factors  : 

(a)  Fundamental  units 2 

(b)  Derived  units 2 

I.  Geometric  and  dynamic  units 2 

II.  Heat  units 3 

III.  Magnetic  and  electric  units 3 

2.  Equivalents  of  metric  and  British  imperial  weights  and  measures : 

(1)  Metric  to  imperial 5 

(2)  Multiples,  metric  to  imperial 6 

(3)  Imperial  to  metric j 

(4)  Multiples,  imperial  to  metric 8 

3.  Tables  for  converting  U.  S.  weights  and  measures  : 

(1)  Customary  to  metric o 

(2)  Metric  to  customary IO 

4.  Factors  for  the  conversion  of  lengths 1 1 

5-         "         "      "          "            "  areas         n 

6.         "         "      "          "            «  volumes 12 

7-         "         "      "          "            "  capacities 12 

8.         "         ^    "          «            «  masses 13 

9-         "         "      "          "            "  moments  of  inertia 13 

10.  "         "      "          «  «  angles 14 

11.  "         "      "          "  «  times 14 

12.  "         "      "          "  "  linear  velocities '.15 

13-  "      "          "  "  angular  velocities 15 

14-  "      "          "  "  momentums 16 

15-  "         "      "          "  "  moments  of  momentum  .  .          16 


Vi  TABLE    OF    CONTENTS.     ' 

16.  Factors  for  the  conversion  of  forces  .............  17 

17.  "         "      "          "             "  linear  accelerations     ........  17 

18.  "         "      "          "             "  angular  accelerations      .......  18 

19.  "         "      "          "            "  linear  and  angular  accelerations  .     .     .     .  i& 

20.  "         "      "          "  "  stress  or  force  per  unit  of  area,  gravitation 

units      ............  19 

21.  "         "      "          •*  "  power,  rate  of  working,  or  activity,  gravi- 

tation units     ..........  19 

22.  "         "      "           "            "  work  or  energy,  gravitation  units      ...  20 

23.  "         "      "          "            "  film  or  surface  tension    .....     .     .  20 

24.  "         "      "          "  "  power,  rate  of  working  or  activity,  absolute 

units      .......     .....  21 

25.  "         "      "  "  "  work  or  energy,  absolute  units     ....21 

26.  "         "      "          "  "   stress  or  force  per  unit  of  area,  absolute 

units      ............  22 

27.  "         "      "          "             "  film  or  surface  tension,  absolute  units    .     .  22 

28.  "         "      "          "             "  densities  ............  23 

29.  "         "      "           "             "   specific  electrical  resistance     .....  23 

30.  "         "      "          "             "   electrolytic  deposition     .......  24 

31.  "         "      "           "             "  heat  units      ...........  24 

32.  "         "      "           "             "  thermometer  scales    ........  25 

33.  "         "      "          "  "  electric  displacement  and  other  quantities 

of  dimensions  M*  L~^      ......  25 

34.  "         "      "          "  "   surface  density  of  magnetization  and  other 

quantities  of  dimensions  M*  L~*    ...  26 

35.  "         "      "  "  "  intensity  of  magnetization  and  other  quan- 

tities of  dimensions  M*  \}    .....  26 

36.  "         "      "          "  "  electric  potential  and  other  quantities  of 

dimensions  M^  iJ  ........  27 

37.  "         "      "          "  "  magnetic  moment  and  other  quantities  of 

dimensions  M*  L^   ........  27 

38.  Values  of         e  —  (hyperbolic  sines)  for  values  of  x  from  o  to  5      ...  28 


39.  «       »        *        (hyperbolic  cosines)  for   "         "       "         "  ...     29 

40.  Logarithms  of  ^^-  —     "         "       "         "        ..........     30 


41.  "         of      ~            "         "                " 31 

42.  Values  of  e*  and  e~x  and  their  logarithms 32 

43.  "       "  ?*  and  <r«*  "       "            "             33 

44.  ««       "^vrand^"       "            «             34 

45-       '  "       "  <&'  and  ^    «             "             34 

46.  "       "  ex  and  e~x  "            "             fractional  values  of  x    .     .     .  35 

47.  Probability  of  errors  of  observation -35 

48.  "           "      "       "          •«             36 


TABLE   OF   CONTENTS. 

49.    Values  of  o.6745t/-  ................    36 

"       "  37 


37 


52.         "       «'  0.8453     .A— 37 


53.  "       "  the  logarithm  of  the  gamma  function  T(n)  for  values  of  n 

between  i  and  2 38 

54.  "       "  the  first  seven  zonal  harmonics  from  0  =  o°  to  #  =  90°  .     .     .  40 

55.  "       "  log  M/i-rr'Vaa1  for  facilitating  the  calculation  of  the  mutual 

inductance  between  two  coaxial  circles 42 

56.  "       "     I  *(i — sin20sina<£)  ~  d$  for  different  values  of  0  with  the  loga- 

rithms of  these  integrals 43 

57.  Cross  section  and  weight  of  copper,  iron,  and  brass  wire  of  different 

diameters,  British  units 44 

58.  Cross  section   and  weight  of  copper,  iron,  and  brass  wire  of  different 

diameters,  metric  units 46 

59.  Cross  section  and  weight  in  various  units  of  aluminium  wires  of  differ- 

ent diameters .  48 

60.  Cross  section  and  weight  in  various  units  of  platinum  wires  of  different 

diameters 50 

61.  Cross  section  and  weight  in  various   units  of  gold   wires  of  different 

diameters 52 

62.  Cross  section   and  weight  in  various  units   of  silver  wires  of  different 

diameters 54 

63.  Weight,  in  grammes  per  square  metre,  of  sheet  metal 56 

64.  "       "   various  British  units,  of  sheet  metal 57 

65.  Size,  weight,  and  electrical  constants  of  copper  wire  according  to  Brown 

and  Sharp's  gauge  and  British  measure 58 

66.  Same  data  as  65,  but  in  metric  measure 60 

67.  "        "     "    "     but  British  standard  wire  gauge 62 

68.  "        "      "  67,  but  in  metric  measure 64 

69.  "        "     "  65,  but  Birmingham  wire  gauge 66 

70.  "        "      "  69,  but  in  metric  measure 68 

71.  Strength  of  materials  : 

(a)  Metals  and  alloys 70 

(b)  Stones  and  bricks 70 

(<r)  Timber 70 

72.  Composition  and  physical  properties  of  steel 71 

73.  Effect  of  the  reduction  of  section  produced  by  rolling  on  the  strength  of 

bar  iron 72 

74.  Effect  of  diameter  on  the  strength  of  bar  iron 72 


Vlil  TABLE   OF    CONTENTS.    ' 

75.  Strength  of  copper-tin  alloys  (bronzes) 73 

76.  "         "  copper-zinc  alloys  (brasses) 73 

77.  "         "  copper-zinc-tin  alloys 73 

78.  Moduli  of  rigidity 74 

79.  Young's  modulus  of  elasticity 75 

80.  Effect  of  temperature  on  rigidity 76 

81.  Values  of  Poisson's  ratio 76 

82.  Elastic  moduli  of  crystals,  formulae       77 

83.  "           "        "        "         numerical  results 78 

84.  Compressibility  of  nitrogen  at  different  pressures  and  temperatures      .  79 

85.  "  "  hydrogen"        "                "            "             "                   .  79 

86.  "  "  methane  "       "                "           "             "                  .  79 

87.  "  "  ethylene   "        "                "            "             "                   .  79 

88.  "  "  carbon  dioxide"               "            "             "  value  oipv  80 

89.  "  "               "            "               "           "             "  values     of 

the  ratio  pvjp^v^ 80 

90.  "  "  air,  oxygen,  and  carbon  monoxide  at  different  pres- 

sures and  ordinary  temperature 80 

91.  "  "  sulphur  dioxide  at  different  pressures  and  tempera- 

tures    8 1 

92.  "  "  ammonia  at  different  pressures  and  temperatures     .  81 

93.  "             and  bulk  moduli  of  liquids 82 

94.  "               "        "          "       "  solids 83 

95.  Density  of  various  solids 84 

96.  "         "        "       alloys .  85 

97.  "         "        "       metals 86 

98.  *'         "        "       woods 87 

99.  "         "        "       liquids 88 

100.  "         "        "       gases " 89 

101.  "         "        "       aqueous  solutions  of  salts 90 

102.  "         "        "       water  between  o°  and  32°  C 92 

103.  Volume  of  water  at  different  temperatures  in  terms  of  its  volume  at 

temperature  of  maximum  density 93 

104.  Density  and  volume  of  water  in  terms  of  the  density  and  volume  at 

4°  C 94 

105.  "           "        "       "    mercury  at  different  temperatures 95 

106.  Specific  gravity  of  aqueous  ethyl  alcohol 96 

107.  Density  of  aqueous  methyl  alcohol 97 

108.  Variation  of  density  of  alcohol  with  temperature 98 

109.  Velocity  of  sound  in  air,  principal  determinations  of 99 

no.          "         "       "       "    solids 100 

in.          "         "       "      "    liquids  and  gases 101 

112.  Force  of  gravity  at  sea  level  and  different  latitudes 102 

113.  Results  of  some  of  the  more  recent  determinations  of  gravity  .     .     .     .103 

114.  Value  of  gravity  at  stations  occupied  by  U.  S.  C.  &  G.  Survey  in  1894  104 

115.  Length  of  seconds  pendulum  for  sea  level  and  different  latitudes      .     .104 

116.  Determinations  of  the  length  of  the  seconds  pendulum 105 


TABLE    OF   CONTENTS.  x 

117.  Miscellaneous  data  as  to  the  earth  and  planets 106 

118.  Aerodynamics  :  Data  for  wind  pressure  and  values  of  J*"mPa  =  fa  P^  108 
ng.                "                Data  for  the  soaring  of  planes 109 

120.  Terrestrial  magnetism,  total  intensity no 

121.  "                "             secular  variation  of  total  intensity no 

122.  "                "             dip in 

123.  "                "             secular  variation  of  dip in 

124.  "                "             horizontal  intensity 112 

125.  "  "             secular  variation  of  horizontal  intensity     .     .     .112 

126.  "  "             formulae  for  value  and  secular  variation  of  dec- 

lination       113 

127.  "  "             secular  variation  of  declination  (eastern  stations)  114 

128.  "  "                  "            "         "          "           (central  stations)  115 

129.  "  "                   "            "         "          "            (western  stations)  116 

130.  "  "             position    of    agonic    line    in   1800,   1850,    1875, 

and  1890 117 

131.  "  "             date  of  maximum  east    declination    at    various 

stations 118 

132.  Tables  for  computing  pressure  of  mercury  and  of  water,  British  and 

metric  measures 119 

133.  Reduction  of  barometric  height  to  standard  temperature 120 

134.  Correction  of  barometer  to  standard  gravity,  British  and  metric  mea- 

sures       121 

135.  Reduction  of  barometer  to  latitude  45°,  British  scale 122 

136.  "           "           "           "         "         "      metric  scale 123 

137.  Correction  of  barometer  for  capillarity,  metric  and  British  measures     .  124 

138.  Absorption  of  gases  by  liquids 125 

139.  Vapor  pressures 126 

140.  Capillarity  and  surface  tension,  water  and  alcohol  in  air 128 

141.  "  "         "             "        miscellaneous  liquids  in  air      .     .     .     .128 

142.  "            "         "             "        aqueous  solutions  of  salts 128 

143.  "  "         "             "        liquids   in  contact  with    air,   water,   or 

mercury 129 

144.  "            "         "             "        liquids  at  solidifying  point 129 

145.  "            "         "             "        thickness  of  soap  films 129 

146.  Colors  of  thin  plates,  Newton's  Rings 130 

147.  Contraction  produced  by  solution  of  salts 131 

148.  "                 "           "    dilution  of  solutions 134 

149.  Coefficients  of  friction 135 

150.  Specific  viscosity  of  water  at  different  temperatures 136 

151.  Coefficients  of  viscosity  for  solutions  of  alcohol  in  water 137 

152.  Specific  viscosity  of  mineral  oils 137 

153.  "             "          "  various     "          137 

154.  "            "         "  various  liquids        138 

155.  "            "         "         "           "      temperature  variation 139 

156.  "  "         "  solutions,  variation  with  density  and  temperature    .  140 

157.  "            "         "           "         atomic  concentrations 144 


X  TADLE    OF    CONTENTS, 

158.  Specific  viscosity  of  gases  and  vapors 145 

159.  "  "       "      formulae  for  temperature  variation  .     .     .     .146 

160.  Diffusion  of  liquids  and  solutions  of  salts  into  water  .     .     .   •  .     .     .     .147 

161.  "         "  vapors 148 

162.  "  gases  and  vapors 149 

163.  Isotonic  coefficients  and  lowering  of  the  freezing-point 150 

164.  Osmotic  pressure 150 

165.  Pressure  of  aqueous  vapor  (Regnault) 151 

166.  "         "         "  "       (Regnault  and  Broch) 154 

167.  Weight  in  grains  of  aqueous  vapor  in  a  cubic  foot  of  saturated  air   .     .155 

168.  "        "  grammes  of    "  "         "       "      metre  of     "  "     .     .  155 

169.  Pressure  of  aqueous  vapor  at  low  temperatures  . 156 

170.  Hygrometry,  vapor  pressure  in  the  atmosphere      .     .     .     ,     .     .„   .     .157 

171.  "  dew-points 158 

172.  Values  of  0.378*?  in  atmospheric  pressure  equation  h—B — 0.378^      .     .  160 

173.  Relative  humidity 160 

174.  Table  for  facilitating  the  calculation  of  /i/j6o 162 

175.  Logarithms  of  /i/j6o  for  values  of  h  between  80  and  800 162 

176.  Values  of  i-\-.oo^6jf : 

(a)  For  values  of  /  between  o°  and  10°  C.  by  tenths 164 

(/;)     "         "       "  /         "    —90°  and  +1990°  C.  by  tens 165 

(c)  Logarithms  for  /      "    — 49°  and  -{-399°  C.  by  units 166 

(</)    "         "       "/        "        400°  and  1990°  C.  by  tens 168 

177.  Determination  of  heights  by  barometer 169 

178.  Barometric  pressures  corresponding  to  different  temperatures  of  the 

boiling-point  of  water  : 

(a)  British  measure 170 

(b)  Metric  measure     .     . 171 

179.  Rowland's  standard  wave-lengths  in  arc  and  sun  spectra 172 

180.  Wave-lengths  of  the  Fraunhofer  lines 175 

181.  Various  determinations  of  the  velocity  of  light 176 

182.  Photometric  standards 176 

183.  Solar  energy  and  its  absorption  by  the  terrestrial  atmosphere  .     .     .     .177 

184.  The  solar  constant 177 

185.  Index  of  refraction  of  glass  : 

(a}  Fraunhofer's  determinations .178- 

(b)  Bailie's  " 178 

(c)  Hopkinson's  "  • 178- 

(//)   Mascart's  "  179 

(<?)    Langley's  "  179 

(/)  Vogel  on  effect  of  temperature 179 

O)   Miiller  "      "       "  "  179 

186.  Indices  of  refraction  for  various  alums 180 

187.  "        "         "  "    metals  and  metallic  oxides : 

(a)  Kundt's  experiments 181 

(b)  Du  Bois  and  Ruben's  experiments 181 

(f)    Drude's  experiments 181 


TABLE    OF   CONTENTS.  XI 

Index  of  refraction  of  rock  salt,  various  authorities 182 

"       "         "  "  sylvine 182 

"       "         "  "  fluor-spar 183 

"       "         "  "  various  monorefringents 184 

"       "         "  "  Iceland  spar 185 

"       "         "  "  quartz 186 

"       "         "  "  various  uniaxial  crystals 187 

«       "         "  "       "        biaxial  crystals 187 

"  "         "           "  solutions  of  salts  and  acids  : 

(a)  Solutions  in  water 188 

(b)  Solutions  in  alcohol 188 

(f)          "  "  potassium  permanganate 188 

Index  of  refraction  of  various  liquids 189 

"       "         "  "   gases  and  vapors 190 

Rotation  of  plane  of  polarized  light  by  solutions .  191 

"         "       "      "         "  "      "    sodium  chlorate  and  by  quartz  .  191 

201.  Lowering  of  freezing-points  by  salts  in  solution 192 

202.  Vapor-pressures  of  solutions  of  salts  in  water 194 

Raising  of  boiling-points  by  salts  in  solution 196 

Thermal  conductivity  of  metals  and  alloys 197 

"  "  "  various  substances 198 

"  "  "  water  and  solutions  of  salts 198 

207.  "  "  "  organic  liquids 198 

208.  "  "  "  gases 198 

209.  Freezing  mixtures 199 

210.  Critical  temperatures,  pressures,  volumes,  and  densities  of  gases  .     .     .  200 
Heat  of  combustion 201 

"      "  combination 202 

Latent  heat  of  vaporization 204 

**         "       "  fusion 206 

Melting-points  of  chemical  elements 207 

Boiling-points  of  "  "  207 

Melting-points  of  various  inorganic  compounds    • 208 

Boiling-points  of         "  "  "  210 

Melting-points  of  mixtures .     . •     .211 

Densities,   melting-points,    and    boiling-points   of   some    organic   com- 
pounds : 

(a)  Paraffin  series 212 

(&)  Olefine  series 212 

(f)    Acetylene  series 212 

(a)  Monatomic  alcohols 213 

(e)   Alcoholic  ethers    .     .     * 213 

(/)  Ethyl  ethers 213 

221.  Coefficients  of  linear  expansion  of  chemical  elements 214 

222.  "  "      "  "  "  miscellaneous  substances    .     .     .     .215 

223.  "  "  cubical  expansion  of  crystalline  and  other  solids   .     .     .216 

224.  "  "        "  "  "  liquids 217 


M 

xii  TABLE   OF    CONTENTS/ 

225.  Coefficients  of  cubical  expansion  of  gases 218 

226.  Dynamical  equivalent  of  the  thermal  unit 219 

227.  "  "  "     "         »  «     historical  table 220 

228.  Specific  heat  of  water,  descriptive  introduction 222 

228.  Specific  heat  of  water 222 

229.  Ratio  of  specific  heats  of  air,  various  determinations 223 

230.  Specific  heats  of  gases  and  vapors 224 

231.  Vapor  pressure  of  ethyl  alcohol 225 

232.  "  "         "   methyl    "        225 

233.  Vapor  pressures  and  temperatures  of  various  liquids : 

(a)  Carbon  disulphide 226 

(£)   Chlorobenzene      .     .     . 226 

(f)   Bromobenzene 226 

(d)  Aniline 226 

(e)  Methyl  salicylate 227 

(f)  Bromonaphthaline 227 

(g)  Mercury 22? 

234.  Thermometers,  comparisons  of  mercury  in  glass  and  air  thermometers  228 

235.  comparison  of  various  kinds  with  hydrogen  thermometer  229 

236.  '•  "         "          "       "      air  thermometer     .     .  229 

237.  change  of  zero  due  to  heating  (Jena  glass) 230 

238.  "  "         "     "        "     "         «       (various  kinds  of  glass)  .  230 

239.  "  "         "     "       "     «         "       effect  of  composition  of 

glass 231 

240.  slow  change  of  zero  with  time    .........  231 

241.  "  correction  for  mercury  in  stem 232 

242.  Emissivity  of  polished  and  blackened  surfaces  in  air  at  ordinary  pres- 

sures      234 

243.  Emissivity  of  polished  and  blackened  surfaces  in  air  at  different  pres- 

sures      234 

244.  Constants  of  emissivity  from  various  substances  to  vacuum      ....  235 

245.  Effect  of  absolute  temperature  of  surface  on  the  emissivity,  constants 

of  bright  and  blackened  platinum  wire 235 

246.  Radiation  of  bright  platinum  wire  to  copper  envelope  across  air  of  dif- 

ferent pressures 236 

247.  Effect  of  pressure  on  radiation  at  different  temperatures      .....  236 

248.  Properties  and  constants  of  saturated  steam,  metric  measure   .     .     .     .  237 

249.  "  "  *'          "         "  "        British  measure  ....  238 

250.  Ratio  of  the  electrostatic  to  the  electromagnetic  unit  of  electricity,  dif- 

ferent determinations  of 243 

251.  Dielectric  strength  : 

(a)  Medium  air  and  terminals  flat  plates 244 

(b)  "         "     "             "         balls  of  different  diameter      ....  244 
(f)          "         "     "             "         balls  comparison  of  the  results  of  dif- 
ferent observers 244 

252.  Dielectric  strength  of  gases,  effect  of  pressure  on .245 

253.  "  "          "  various  substances 245 


TABLE    OF    CONTENTS.  Xlll 

254.  Data  as  to  electric  battery  cells  : 

(a)  Double  fluid  batteries , 246 

(b)  Single  fluid  batteries 247 

(c)  Standard  cells 247 

(d)  Secondary  cells 247 

255.  Thermoelectric  power  of  various  metals  and  alloys 24$ 

256.  "                 "        "        "        alloys 249 

257.  Thermoelectric  neutral  point  of  various  metals  relative  to  lead     .     .     .  249 

258.  Specific  heat  of  electricity  for  metals 249 

259.  Thermoelectric  power  of  metals  and  solutions 250 

260.  Peltier  effect,  Jahn's  experiments 250 

261.  "          "      Le  Roux's    " 250 

262.  Conductivity  of  three-metal  and  miscellaneous  alloys 251 

263.  "               "  alloys 252 

264.  Specific  resistance  of  metallic  wires,  various  dimension  units  ....  254 

265.  "              "           "  metals,  various  authorities 255 

266.  "               "           "      "       and  alloys  at  low  temperatures 256 

267.  Effect  of  elastic  and  permanent  elongation  on  resistance  of  metallic 

wires 258 

268.  Resistance  of  wires  of  different  diameter  to  alternating  currents  .     .     .258 

269.  Conductivity  of  dilute  solutions  proportional  to  amount  of  dissolved  salt  259 

270.  Electrochemical  equivalent  numbers  and  densities  of  approximately  nor- 

mal solutions 259 

Specific  molecular  conductivities  of  solutions 260 

Limiting  values  of  specific  molecular  conductivities 261 

Temperature  coefficients  of  dilute  solutions 261 

Various  determinations  of  the  ohm,  the  electrochemical  equivalent  of 

silver  and  the  electromotive  force  of  the  Clark  cell 262 

Specific  inductive  capacity  of  gases 263 

"  solids 264 

"  "  liquids 265 

Contact  difference  of  potential,  solids  with  liquids  and  liquids  with 

liquids  in  air 266 

279.  Contact  difference  of  potential,  solids  with  solids  in  air 268 

280.  Potential  difference  between  metals  in  various  solutions 269 

281.  Resistance  of  glass  and  porcelain  at  different  temperatures      ....  270 

282.  Relation  between  thermal  and  electrical  conductivities  : 

(a)   Arbitrary  units 271 

(£)   Values  in  c.  g.  s.  units       271 

(c)  Berget's  experiments 271 

(d)  Kohlrausch's  results 271 

283.  Electrochemical  equivalents  and  atomic  weights  of  the  chemical  ele- 

ments   272 

284.  Permeability  of  iron  for  various  inductions 274 

285.  Permeability  of  transformer  iron  : 

(a]  Specimen  of  Westinghouse  No.  8  transformer 274 

(V)            "         "             "               "6           "            275 


XIV  TABLE    OF    CONTENTS. 

(r)    Specimen  of  Westinghouse  No.  4  transformer  275 

(d)  "         "    Thomson-Houston  i5oo-watt  transformer  ....  275 

286.  Composition  and  magnetic  properties  of  iron  and  steel    .     .     .     .     .     .276 

287.  Permeability  of  some  specimens  in  Table  286 278 

288.  Magnetic  properties  of  soft  iron  at  o°  and  100°  C 278 

289.  "  "  "  steel  at  o°  and  100°  C 278 

290.  "  "  "  cobalt  at  100°  C 279 

291.  "  "  "  niclcel  at  100°  C 279 

292.  "  "  "  magnetite 279 

293.  "  "  "  Lowmoor  wrought  iron  in  intense  fields    .     .     .279 

294.  "  "  "  Vicker's  tool  steel  in  intense  fields 279 

295.  "  "  "  Hadfield's  manganese  steel  in  intense  fields  .     .279 

296.  Saturation  values  for  different  steels 279 

297.  Magnetic  properties  of  very  weak  fields 280 

298.  Dissipation  of  energy  in  the  cyclic  magnetization  of  magnetic  substances  280 

299.  "  "  "  "  "  "  "  "  cable  transformers  .  280 

300.  "  "  "  "  "  "  "  "  various  substances  .  281 

301.  "  "  ''  "  "  "  "  "  transformer  cores     .  282 

302.  "  "  "  "  "  "  "  "  various  specimens  of 

soft  iron    .  .     .     .283 

Magneto-optic  rotation,  Verdet's  constant 284 

303.  "                "          in  solids 285 

304.  "                "           "  liquids 286 

305.  "                "           "  solutions  of  acids  and  salts  in  water     .     .     .  288 

306.  "                "           "         "         "  salts  in  alcohol 290 

307.  "                "           "         "     in  hydrochloric  acid    ......  290 

308.  "                "           "gases • 291 

309.  Miscellaneous  values  of  Verdet's  and  Kundt's  constants     .    -.     .     .     .291 

310.  "  "        u  susceptibility  for  liquids  and  gases      ....  292 

311.  Kerr's  constants  for  iron,  nickel,  cobalt,  and  magnetite 292 

312.  Effect  of  magnetic  field  on  the  electric  resistance  of  bismuth  (initial 

resistance  of  one  ohm  for  zero  field  and  various  temperatures)     .     .  293 

313.  Effect  of  magnetic  field  on  the  electric  resistance  of  bismuth  (initial 

resistance  one  ohm  for  zero  field  and  temperature  zero  Centigrade)  293 

3^4.    Specific  heat  of  various  solids  and  liquids •*  .     .  294 

315.    Specific  heat  of  metals 296 


INTRODUCTION. 


UNITS   OF   MEASUREMENT   AND   CONVERSION   FORMULAE. 

Units.  —  The  quantitative  measure  of  anything  is  a  number  which  expresses  the 
ratio  of  the  magnitude  of  the  thing  to  the  magnitude  of  some  other  thing  of  the 
same  kind.  In  order  that  the  number  expressing  the  measure  may  be  intelligi- 
ble, the  magnitude  of  the  thing  used  for  comparison  must  be  known.  This  leads 
to  the  conventional  choice  of  certain  magnitudes  as  units  of  measurement,  and 
any  other  magnitude  is  then  simply  expressed  by  a  number  which  tells  how  many 
magnitudes  equal  to  the  unit  of  the  same  kind  of  magnitude  it  contains.  For 
example,  the  distance  between  two  places  may  be  stated  as  a  certain  number  of 
miles  or  of  yards  or  of  feet.  In  the  first  case,  the  mile  is  assumed  as  a  known 
distance ;  in  the  second,  the  yard,  and  in  the  third,  the  foot.  What  is  sought  for 
in  the  statement  is  to  convey  an  idea  of  the  distance  by  describing  it  in  terms  of 
distances  which  are  either  familiar  or  easily  referred  to  for  comparison.  Similarly 
quantities  of  matter  are  referred  to  as  so  many  tons  or  pounds  or  grains  and  so 
forth,  and  intervals  of  time  as  a  number  of  hours  or  minutes  or  seconds.  Gen- 
erally in  ordinary  affairs  such  statements  appeal  to  experience ;  but,  whether  this 
be  so  or  not,  the  statement  must  involve  some  magnitude  as  a  fundamental  quan- 
tity, and  this  must  be  of  such  a  character  that,  if  it  is  not  known,  it  can  be  readily 
referred  to.  We  become  familiar  with  the  length  of  a  mile  by  walking  over  dis- 
tances expressed  in  miles,  with  the  length  of  a  yard  or  a  foot  by  examining  a  yard 
or  a  foot  measure  and  comparing  it  with  something  easily  referred  to,  —  say  our 
own  height,  the  length  of  our  foot  or  step,  —  and  similarly  for  quantities  of  other 
kinds.  This  leads  us  to  be  able  to  form  a  mental  picture  of  such  magnitudes 
when  the  numbers  expressing  them  are  stated,  and  hence  to  follow  intelligently 
descriptions  of  the  results  of  scientific  work.  The  possession  of  copies  of  the 
units  enables  us  by  proper  comparisons  to  find  the  magnitude-numbers  express- 
ing physical,  quantities  for  ourselves.  The  numbers  descriptive  of  any  quan- 
tity must  depend  on  the  intrinsic  magnitude  of  the  unit  in  terms  of  which  it  is 
described.  Thus  a  mile  is  1760  yards,  or  5280  feet, -and  hence  when  a  mile  is 
taken  as  the  unit  the  magnitude-number  for  the  distance  is  i,  when  a  yard  is  taken 
as  the  unit  the  magnitude-number  is  1760,  and  when  a  foot  is  taken  it  is  5280. 
Thus,  to  obtain  the  magnitude-number  for  a  quantity  in  terms  of  a  new  unit  when 
it  is  already  known  in  terms  of  another  we  have  to  multiply  the  old  magnitude- 
number  by  the  ratio  of  the  intrinsic  values  of  the  old  and  new  units ;  that  is,  by 
the  number  of  the  new  units  required  to  make  one  of  the  old. 


XVI  INTRODUCTION. 

Fundamental  Units  of  Length  and  Mass.  —  It  is  desirable  that  as  few  dif- 
ferent kinds  of  unit  quantities  as  possible  should  be  introduced  into  our  measure- 
ments, and  since  it  has  been  found  possible  and  convenient  to  express  a  large 
number  of  physical  quantities  in  terms  of  length  or  mass  or  time  units  and  com- 
binations of  these  they  have  been  very  generally  adopted  as  fundamental  units. 
Two  systems  of  such  units  are  used  in  this  country  for  scientific  measurements, 
namely,  the  British  and  the  French,  or  metric,  systems.  Tables  of  conversion 
factors  are  given  in  the  book  for  facilitating  comparisons  between  quantities  ex- 
pressed in  terms  of  one  system  with  similar  quantities  expressed  in  the  other.  In 
the  British  system  the  standard  unit  of  length  is  the  yard,  and  it  is  defined  as  fol- 
lows :  "  The  straight  line  or  distance  between  the  transverse  lines  in  the  two  gold 
plugs  in  the  bronze  bar  deposited  in  the  Office  of  the  Exchequer  shall  be  the  gen- 
uine Standard  of  Length  at  62°  F.,  and  if  lost  it  shall  be  replaced  by  means  of  its 
copies."  [The  authorized  copies  here  referred  to  are  preserved  at  the  Royal 
Mint,  the  Royal  Society  of  London,  the  Royal  Observatory  at  Greenwich,  and  the 
New  Palace  at  Westminster.] 

The  British  standard  unit  of  mass  is  the  pound  avoirdupois,  and  is  the  mass  of 
a  piece  of  platinum  marked  "  P.  S.  1844,  i  lb.,"  which  is  preserved  in  the  Exchequer 
Office.  Authorized  copies  of  this  standard  are  kept  at  the  same  places  as  those 
of  the  standard  of  length. 

In  the  metric  system  the  standard  of  length  is  defined  as  the  distance  between 
the  ends  of  a  certain  platinum  bar  (the  metre  des  Archives]  when  the  whole  bar  is 
at  the  temperature  o°  Centigrade.  The  bar  was  made  by  Borda,  and  is  preserved 
in  the  national  archives  of  France.  A  line-standard  metre  has  been  constructed 
by  the  International  Bureau  of  Weights  and  Measures,  and  is  known  as  the  Inter- 
national Prototype  Metre.  This  standard  is  of  the  same  length  as  the  Borda  stand- 
ard. A  number  of  standard-metre  bars  which  have  been  carefully  compared  with 
the  International  Prototype  have  lately  been  made  by  the  International  Bureau  of 
Weights  and  Measures  and  furnished  to  the  various  governments  who  have  con- 
tributed to  the  support  of  that  bureau.  These  copies  are  called  National  Proto- 
types. 

Borda,  Delambre,  Laplace,  and  others,  acting  as  a  committee  cf  the  French 
Academy,  recommended  that  the  standard  unit  of  length  should  be  the  ten  mil- 
lionth part  of  the  length,  from  the  equator  to  the  pole,  of  the  meridian  passing 
through  Paris.  In  1795  the  French  Republic  passed  a  decree  making  this  the 
legal  standard  of  length,  and  an  arc  of  the  meridian  extending  from  Dunkirk  to 
Barcelona  was  measured  by  Delambre  and  Mechain  for  the  purpose  of  realizing 
the  standard.  From  the  results  of  that  measurement  the  metre  bar  was  made 
by  Borda.  The  metre  is  not  now  defined  as  stated  above,  but  as  the  length  of 
Borda's  rod,  and  hence  subsequent  measurements  of  the  length  of  the  meridian 
have  not  affected  the  length  of  the  metre. 

The  French,  or  metric,  standard  of  mass,  the  kilogramme,  is  the  mass  of  a 
piece  of  platinum  also  made  by  Borda  in  accordance  with  the  same  decree  of  the 
Republic.  It  was  connected  with  the  standard  of  length  by  being  made  as  nearly 
as  possible  of  the  same  mass  as  that  of  a  cubic  decimetre  of  distilled  water  at 
the  temperature  of  4°  C.,  or  nearly  the  temperature  of  maximum  density. 

As  in  the  case  of  the  metre,  the  International  Bureau  of  Weights  and  Measures 


INTRODUCTION.  XVH 

has  made  copies  of  the  kilogramme.  One  of  these  is  taken  as  standard,  and  is 
called  the  International  Prototype  Kilogramme.  The  others  were  distributed  in 
the  same  manner  as  the  metre  standards,  and  are  called  National  Prototypes. 

Comparisons  of  the  French  and  British  standards  are  given  in  tabular  form 
in  Table  2  ;  and  similarly  Table  3,  differing  slightly  from  the  British,  gives  the 
legal  ratios  in  the  United  States.  In  the  metric  system  the  decimal  subdivi- 
sion is  used,  and  thus  we  have  the  decimetre,  the  centimetre,  and  the  millimetre  as 
subdivisions,  and  the  dekametre,  hektometre,  and  kilometre  as  multiples.  The 
centimetre  is  most  commonly  used  in  scientific  work. 

Time.  —  The  unit  of  time  in  both  the  systems  here  referred  to  is  the  mean 
solar  second,  or  the  86,4ooth  part  of  the  mean  solar  day.  The  unit  of  time  is 
thus  founded  on  the  average  time  required  for  the  earth  to  make  one  revolution 
on  its  axis  relatively  to  the  sun  as  a  fixed  point  of  reference. 

Derived  Units.  — Units  of  quantities  depending  on  powers  greater  than  unity 
of  the  fundamental  length,  mass,  and  time  units,  or  oh  combinations  of  different 
powers  of  these  units,  are  called  "  derived  units."  Thus,  the  unit  of  area  and  of 
volume  are  respectively  the  area  of  a  square  whose  side  is  the  unit  of  length  and 
the  volume  of  a  cube  whose  edge  is  the  unit  of  length.  Suppose  that  the  area  of 
a  surface  is  expressed  in  terms  of  the  foot  as  fundamental  unit,  and  we  wish  to 
find  the  area-number  when  the  yard  is  taken  as  fundamental  unit.  The  yard  is 
3  times  as  long  as  the  foot,  and  therefore  the  area  of  a  square  whose  side  is  a 
yard  is  3  X  3  times  as  great  as  that  whose  side  is  a  foot.  Thus,  the  surface  will 
only  make  one  ninth  as  many  units  of  area  when  the  yard  is  the  unit  of  length  as 
it  will  make  when  the  foot  is  that  unit.  To  transform,  then,  from  the  foot  as  old 
unit  to  the  yard  as  new  unit,  we  have  to  multiply  the  old  area-number  by  1/9,  or  by 
the  ratio  of  the  magnitude  of  the  old  to  that  of  the  new  unit  of  area.  This  is  the 
same  rule  as  that  given  above,  but  it  is  usually  more  convenient  to  express  the 
transformations  in  terms  of  the  fundamental  units  directly.  In  the  above  case, 
since  on  the  method  of  measurement  here  adopted  an  area-number  is  the  product 
of  a  length-number  by  a  length-number  the  ratio  of  two  units  is  the  square  of  the 
ratio  of  the  intrinsic  values  of  the  two  units  of  length.  Hence,  if  /  be  the  ratio 
of  the  magnitude  of  the  old  to  that  of  the  new  unit  of  length,  the  ratio  of  the  cor- 
responding units  of  area  is  /2.  Similarly  the  ratio  of  two  units  of  volume  will  be 
/3,  and  so  on  for  other  quantities. 

Dimensional  Formulae.  —  It  is  convenient  to  adopt  symbols  for  the  ratios 
of  length  units,  mass  units,  and  time  units,  and  adhere  to  their  use  throughout ; 
and  in  what  follows,  the  small  letters,  /,  ;/z,  /,  will  be  used  for  these  ratios.  These 
letters  will  always  represent  simple  numbers,  but  the  magnitude  of  the  number 
will  depend  on  the  relative  magnitudes  of  the  units  the  ratios  of  which  they  repre- 
sent. When  the  values  of  the  numbers  represented  by  /,  m,  t  are  known,  and  the 
powers  of  /,  m,  and  /  involved  in  any  particular  unit  are  also  known,  the  factor  for 
transformation  is  at  once  obtained.  Thus,  in  the  above  example,  the  value  of  / 
was  1/3  and  the  power  of  /involved  in  the  expression  for  area  is  T2;  hence,  the 
factor  for  transforming  from  square  feet  to  square  yards  is  1/9.  These  factors 


XV111  INTRODUCTION. 

have  been  called  by  Prof.  James  Thomson  "change  ratios,"  which  seems  an 
appropriate  term.  The  term  "  conversion  factor  "  is  perhaps  more  generally 
known,  and  has  been  used  throughout  this  book. 

Conversion  Factor.  —  In  order  to  determine  the  symbolic  expression  for  the 
conversion  factor  for  any  physical  quantity,  it  is  sufficient  to  determine  the  degree 
to  which  the  quantities  length,  mass,  and  time  are  involved  in  the  quantity.  Thus, 
a  velocity  is  expressed  by  the  ratio  of  the  number  representing  a  length  to  that 
representing  an  interval  of  time,  or  L/T,  an  acceleration  by  a  velocity-number 
divided  by  an  interval  of  time-number,  or  L/T2,  and  so  on,  and  the  correspond- 
ing ratios  of  units  must  therefore  enter  to  precisely  the  same  degree.  The  fac- 
tors would  thus  be  for  the  above  cases,  ///  and  ///2.  Equations  of  the  form  above 
given  for  velocity  and  acceleration  which  show  the  dimensions  of  the  quantity  in 
terms  of  the  fundamental  units  are  called  "  dimensional  equations."  Thus 

E  =  ML2T-2 

is  the  dimensional  equation  for  energy,  and  MLaT~2  is  the  dimensional  formula 
for  energy. 

In  general,  if  we  have  an  equation  for  a  physical  quantity 


where  C  is  a  constant  and  LMT  represents  length,  mass,  and  time  in  terms  of  one 
set  of  units,  and  we  wish  to  transform  to  another  set  of  units  in  terms  of  which 

LMT 

the  length,  mass,  and  time  are  LyM-Ty,  we  have  to  find  the  value  of  --',—',—  ',  which 

LMT 

in  accordance  with  the  convention  adopted  above  will  be  //#*//,  or  the  ratios  of 
the  magnitudes  of  the  old  to  those  of  the  new  units. 

Thus  L,  —  L/,  Mt  =  Mm,  Tj  =  Tt,  and  if  Qy  be  the  new  quantity-number 

Q^CL/'M/OY 

=  CLVaM  VT7C  =  Qtt»V, 

or  the  conversion  factor  is  lanPf,  a  quantity  of  precisely  the  same  form  as  the 
dimension  formula  LaM6Tc. 

We  now  proceed  to  form  the  dimensional  and  conversion  factor  formulae  for 
the  more  commonly  occurring  derived  units. 

1.  Area.  —  The  unit  of  area  is  the  square  the  side  of  which  is  measured  by 
the  unit  of  length.     The  area  of  a  surface  is  therefore  expressed  as 

S  =  CL'2, 

where  C  is  a  constant  depending  on  the  shape  of  the  boundary  of  the  surface 
and  L  a  linear  dimension.  For  example,  if  the  surface  be  square  and  L  be  the 
length  of  a  side  C  is  unity.  If  the  boundary  be  a  circle  and  L  be  a  diameter 
C  =  7r/4,  and  so  on.  The  dimensional  formula  is  thus  L2,  and  the  conversion 
factor  l'\ 

2.  Volume.  —  The  unit  of  volume  is  the  volume  of  a  cube  the  edge  of  which 
is  measured  by  the  unit  of  length.    The  volume  of  a  body  is  therefore  expressed  as 


INTRODUCTION.  XIX 

V  =  CL3, 

where  as  before  C  is  a  constant  depending  on  the  shape  of  the  boundary.     The 
dimensional  formula  is  L3  and  the  conversion  factor  /3. 

3.  Density.  —  The  density  of  a  substance  is  the  quantity  of  matter  in  the  unit 
of  volume.     The  dimension   formula  is  therefore  M/V  or  ML~8,  and  conversion 
factor  ml~*. 

Example.  —  The  density  of  a  body  is  150  in  pounds  per  cubic  foot:  required 
the  density  in  grains  per  cubic  inch. 

Here  m  is  the  number  of  grains  in  a  pound  =  7000,  and  /  is  the  number  of 
inches  in  a  foot=  12  ;  /.  ml~~*  —  yooo/123  —  4.051.  Hence  the  density  is  150  X 
4.051  =607.6  in  grains  per  cubic  inch. 

NOTE.  —  The  specific  gravity  of  a  body  is  the  ratio  of  its  density  to  the  density  of  a  standard 
substance.  The  dimension  formula  and  conversion  factor  are  therefore  both  unity. 

4.  Velocity.  —  The  velocity  of  a  body  at  any  instant  is  given  by  the  equation 
7,'  =  -- -,  or  velocity  is  the  ratio  of  a  length-number  to  a  time-number.     The  di- 
mension formula  is  LT"1,  and  the  conversion  factor  //-1. 

Example.  —  A  train  has  a  velocity  of  60  miles  an  hour :  what  is  its  velocity  in 
feet  per  second  ? 

Here  /==  c 280  and  t  —  3600;  .'.  //-1  =  ££??  =  1*  =1.467.     Hence  the  vt-lo- 

3600       30 

city  =  60  X  1-467  —  88.0  in  feet  per  second. 

5.  Angle.  — An  angle  is  measured  by  the  ratio  of  the  length  of  an  arc  to  the 
length  of  the  'radius  of  the  arc.     The  dimension  formula  and  the  conversion 
factor  are  therefore  both  unity. 

6.  Angular  Velocity.  —  Angular  velocity  is  the  ratio  of  the  magnitude  of  the 
angle  described  in  an  interval  of  time  to  the  length  of  the  interval.     The  dimen- 
sion formula  is  therefore  T"1,  and  the  conversion  factor  is  f~\ 

7.  Linear  Acceleration. — Acceleration  is  the  rate  of  change  of  velocity  or 

a,  =  — •     The  dimension  formula  is  therefore  VT"1  or  LT~2,  and  the  conversion 
dt 

factor  is  /r2. 

Example: —  A  body  acquires  velocity  at  a  uniform  rate,  and  at  the  end  of  one 
minute  is  moving  at  the  rate  of  20  kilometres  per  hour :  what  is  the  acceleration 
in  centimetres  per  second  per  second  ? 

Since  the  velocity  gained  was  20  kilometres  per  hour  in  one  minute,  the  accel- 
eration was  1200  kilometres  per  hour  per  hour. 

Here /=  100000  and  /=36oo;  /.  //~2  =  100000/3600'  =  . 00771,  and  there- 
fore acceleration  =  .007 7 1  X  1200  =  9.26  centimetres  per  second. 

8.  Angular  Acceleration.  — Angular  acceleration  is  rate  of  change  of  angu- 


XX  INTRODUCTION. 

lar  velocity.     The  dimensional  formula  is  thus  angularjrelocity  or  T"2,  and  the 

J. 

conversion  factor  /~2. 

9.  Solid  Angle.  —  A  solid  angle  is  measured  by  the  ratio  of  the  surface  of 
the  portion  of  a  sphere  enclosed  by  the  conical  surface  forming  the  angle  to  the 
square  of  radius  of  the  spherical  surface,  the  centre  of  the  sphere  being  at  the 

vertex  of  the  cone.     The  dimensional  formula  is  therefore  ^-^  or  i,  and  hence 
the  conversion  factor  is  also  i. 

10.  Curvature.  —  Curvature  is  measured  by  the  rate  of  change  of  direction  of 
the  curve  with  reference  to  distance  measured  along  the  curve  as  independent 

variable.     The  dimension  formula  is  therefore    ang  e  or  Lr1,  and  the  conversion 

length 

factor  is  I"1. 

11.  Tortuosity.  —  Tortuosity  is  measured  by  the  rate  of  rotation  of  the  tan- 
gent plane  round  the  tangent  to  the  curve  of  reference  when  length  along  the 

curve  is  independent  variable.     The  dimension  formula  is  therefore   ,  n^  •  or 

length 

I/""1,  and  the  conversion  factor  is  f~1. 

12.  Specific  Curvature  of  a  Surface.  —  This  was  defined  by  Gauss  to  be» 
at  any  point  of  the  surface,  the  ratio  of  the  solid  angle  enclosed  by  a  surface 
formed  by  moving  a  normal  to  the  surface  round  the  periphery  of  a  small  area 
containing  the  point,  to  the  magnitude  of  the  area.     The  dimensional  formula  is 

therefore ^—  or  L~2  and  the  conversion  factor  is  thus  /~2. 

surface 

13.  Momentum.  —  This  is  quantity  of  motion  in  the  Newtonian  sense,  and  is, 
at  any  instant,  measured  by  the  product  of  the  mass-number  and  the  velocity- 
number  for  the  body. 

Thus  the  dimension  formula  is  MV  or  MLT"1,  and  the  conversion  factor  mtt~l. 

Example.  —  A  mass  of  10  pounds  is  moving  with  a  velocity  of  30  feet  per  sec- 
ond :  what  is  its  momentum  when  the  centimetre,  the  gramme,  and  the  second  are 
fundamental  units  ? 

Here  m  =  453-59.  /=  30.48,  and  /=i;  .-.  mfrl  =  453-59  X  30-48  —  13825. 
The  momentum  is  thus  13825  X  10X30  =  4  147  500. 

14.  Moment  of  Momentum.  —  The  moment  of  momentum  of  a  body  with 
reference  to  a  point  is  the  product  of  its   momentum-number  and  the  number 
expressing  the  distance  of  its  line  of  motion  from  the  point.     The  dimensional 
formula  is  thus  MI/T"1,  and  hence  the  conversion  factor  is  w/2/"1. 

15.  Moment  of  Inertia.  — The  moment  of  inertia  of  a  body  round  any  axis 
is  expressed  by  the  formula  2,mr2,  where  m  is  the  mass  of  any  particle  of  the  body 


INTRODUCTION.  XXI 

and  r  its  distance  from  the  axis.  The  dimension  formula  for  the  sum  is  clearly 
the  same  as  for  each  element,  and  hence  is  ML2.  The  conversion  factor  is  there- 
fore m!'2. 

16.  Angular  Momentum.  —  The  angular  momentum  of  a  body  round  any 
axis  is  the  product  of  the  numbers  expressing  the  moment  of  inertia  and  the 
angular  velocity  of  the  body.     The  dimensional  formula  and  the  conversion  fac- 
tor are  therefore  the  same  as  for  moment  of  momentum  given  above. 

17.  Force.  —  A  force  is  measured  by  the  rate  of  change  of  momentum  it  is 
capable   of  producing.      The  dimension  formulae  for  force    and   "  time  rate  of 
change  of  momentum  "  are  therefore  the  same,  and  are  expressed  by  the  ratio 
of  momentum-number  to  time-number  or  MLT~2.     The  conversion  factor  is  thus 


NOTE.  —  When  mass  is  expressed  in  pounds,  length  in  feet,  and  time  in  seconds,  the  unit  force 
is  called  the  poundal.  When  grammes,  centimetres,  and  seconds  are  the  corresponding  units  the 
unit  of  force  is  called  the  dyne. 

Example.     Find  the  number  of  dynes  in  25  poundals. 

Here  m  =  453-59>  '=  3°-48,  and  t=  i  ;  /.  ^#-2=453.59  X  3°-48  =  13825 
nearly.  The  number  of  dynes  is  thus  13825  X  25  —  345625  approximately. 

18.  Moment  of  a  Couple,  Torque,  or  Twisting  Motive.  —  These  are  dif- 
ferent names  for  a  quantity  which  can  be  expressed  as  the  product  of  two  numbers 
representing  a  force  and  a  length.     The  dimension  formula  is  therefore  FL  or 
ML2T~2,  and  the  conversion  factor  is  ml'2t~z. 

19.  Intensity  of  a  Stress.  —  The  intensity  of  a  stress  is  the  ratio  of  the  num- 
ber expressing  the  total  stress  to  the  number  expressing  the  area  over  which  the 
stress  is  distributed.     The  dimensional  formula  is  thus  FL~2  or  ML^T"2,  and  the 
conversion  factor  is  mt~lt~2. 

20.  Intensity  of  Attraction,  or  "  Force  at  a  Point."  —  This  is  the  force  of 
attraction  per  unit  mass  on  a  body  placed  at  the  point,  and  the  dimensional  for- 
mula is  therefore  FM"1  or  LT~2,  the  same  as  acceleration.     The  conversion  fac- 
tors for  acceleration  therefore  apply. 

21.  Absolute  Force  of  a  Centre  of  Attraction,  or  "  Strength  of  a  Cen- 
tre." —  This  is  the  intensity  of  force  at  unit  distance  from  the  centre,  and  is  there- 
fore the  force  per  unit  mass  at  any  point  multiplied  by  the  square  of  the  distance 
from  the  centre.    The  dimensional  formula  thus  becomes  FI^M"1  or  L8T~2.    The 
conversion  factor  is  therefore  /V~2. 

22.  Modulus  of  Elasticity.  —  A  modulus  of  elasticity  is  the  ratio  of  stress 
intensity  to  percentage  strain.     The  dimension  of  percentage  strain  is  a  length 
divided  by  a  length,  and  is  therefore  unity.     Hence,  the  dimensional  formula  of  a 
modulus  of  elasticity  is  the  same  as  that  of  stress  intensity,  or  ML-1T~2,  and  the 
conversion  factor  is  thus  also 


Xxii  INTRODUCTION. 

23.  Work  and  Energy.  —  When  the  point  of  application  of  a  force,  acting  on 
a  body,  moves  in  the  direction  of  the  force,  work  is  done  by  the  force,  and  the 
amount  is  measured  by  the  product  of  the  force  and  displacement  numbers.    The 
dimensional  formula  is  therefore  FL  or  ML2T~2. 

The  work  done  by  the  force  either  produces  a  change  in  the  velocity  of  the  body 
or  a  change  of  shape  or  configuration  of  the  body,  or  both.  In  the  first  case  it 
produces  a  change  of  kinetic  energy,  in  the  second  a  change  of  potential  energy. 
The  dimension  formulae  of  energy  and  work,  representing  quantities  of  the  same 
kind,  are  identical,  and  the  conversion  factor  for  both  is  ml'2t~*. 

24.  Resilience.  —  This  is  the  work  done  per  unit  volume  of  a  body  in  distort- 
ing it  to  the  elastic  limit  or  in  producing  rupture.    The  dimension  formula  is  there- 
fore ML2T-2L~8  01  ML^T-2,  and  the  conversion  factor  mt^r*. 


25.  Power,  or  Activity.  —  Power  —  or,  as  it  is  now  very  commonly  called,  ac- 
tivity —  is  defined  as  the  time  rate  of  doing  work,  or  it  W  represent  work  and  P  power 

p  —  ^.     The  dimensional  formula  is  therefore  WT"1  or  ML2T~3,  and  the  con- 
at 

version  factor  ^z/2/~8,  or  for  problems  in  gravitation  units  more  conveniently/?/"1,, 
where  f  stands  for  the  force  factor. 

Examples,     (a)  Find  the  number  of  gramme  centimetres  in  one  foot  pound. 

Here  the  units  of  force  are  the  attraction  of  the  earth  on  the  pound*  and 
the  gramme  of  matter,  and  the  conversion  factor  is//,  where/  is  453.59  and  /is 
30.48. 

Hence  the  number  is  453.59  X  30.48  =  13825. 

(H)  Find  the  number  of  foot  poundals  in  i  oooooo  centimetre  dynes. 
Here  m  =  1/453.59,  /=  1/30.48,  and  t  =.  i  ;  /.  mt*r*  =  1/453-59  X  3°-482> 
and  ioW2/-2  =  107453.59  X  3°-482  =  2.373. 

(c)  If  gravity  produces  an  acceleration  of  32.2  feet  per  second  per  second,  how 
many  watts  are  required  to  make  one  horse-power  ? 

One  horse-power  is  550  foot  pounds  per  second,  or  550  X  32.2  =  17710  foot 
poundals  per  second.  One  watt  is  io7  ergs  per  second,  that  is,  io7  dyne  centi- 
metres per  second.  The  conversion  factor  is  w/2/"8,  where  m  =  453.59,  /=  30-48r 
and  /=  i,  and  the  result  has  to  be  divided  by  io7,  the  number  of  dyne  centime- 
tres per  second  in  the  watt. 

Hence,  177  lamPr*/!*?—  17710  X  453-59  X  30.487  io7  r=  746.3. 


(d)  How  many  gramme  centimetres  per  second  correspond  to  33000  foot 
pounds  per  minute  ? 

The  conversion  factor  suitable  for  this  case  is///"1,  where/  is  453.59,  ^s  3°"4-8> 
and  /  is  60. 

Hence,  33000  lt~lz=.  33000  X  453-59  X  30.48/60=  7604000  nearly. 

*  It  is  important  to  remember  that  in  problems  like  that  here  given  the  term  "  pound  "  or 
*  gramme  "  refers  to  force  and  not  to  mass. 


INTRODUCTION. 


HEAT   UNITS.  • 

1.  If  heat  be  measured  in  dynamical  units  its  dimensions  are  the  same  as  those 
of  energy,  namely  ML2T~2.      The  most  common  measurements,  however,  are 
made  in  thermal  units,  that  is,  in  terms  of  the  amount  of  heat  required  to  raise 
the  temperature  of  unit  mass  of  water  one  degree  of  temperature  at  some  stated 
temperature.     This  method  of  measurement  involves  the  unit  of  mass  and  some 
unit  of  temperature,  arid  hence  if  we  denote  temperature-numbers  by  ®  and  their 
conversion  factors  by  0  the  dimensional  formula  and  conversion  factor  for  quan- 
tity of  heat  will  be  M®  and  mO  respectively.     The  relative  amount  of  heat  com- 
pared with  water  as  standard  substance  required  to  raise  unit  mass  of  different 
substances  one  degree  in  temperature  is  called  their  specific  heat,  and  is  a  simple 
number. 

Unit  volume  is  sometimes  used  instead  of  unit  mass  in  the  measurement  of 
heat,  the  units  being  then  called  thermometric  units.  The  dimensional  formula 
is  in  that  case  changed  by  the  substitution  of  volume  for  mass,  and  becomes  L8®, 
and  hence  the  conversion  factor  is  to  be  calculated  from  the  formula  1ZQ. 

For  other  physical  quantities  involving  heat  we  have  :  — 

2.  Coefficient  of  Expansion.  —  The  coefficient  of  expansion  of  a  substance 
is  equal  to  the  ratio  of  the  change  of  length  per  unit  length  (linear),  or  change 
of  volume  per  unit  volume  (voluminal)  to  the  change  of  temperature.     These 
ratios  are  simple  numbers,  and  the  change  of  temperature  is  inversely  as  the  mag- 
nitude of  the  unit  of  temperature.     Hence  the  dimensional  and  conversion-factor 
formulae  are  0"1  and  &~\ 

3.  Conductivity,  or  Specific  Conductance.  —  This  is  the  quantity  of  heat 
transmitted  per  unit  of  time  per  unit  of  surface  per  unit  of  temperature  gradient. 
The  equation  for  conductivity  is  therefore,  with  H  as  quantity  of  heat, 

K__     H 

®L2T 
L 

TT  '    -vr 

and  the  dimensional  formula  —  —  =  —  -,  which  gives  ml~lt~l  for  conversion  factor. 


In  thermometric  units  the  formula  becomes  L2T~"1,  which  properly  represents 
diffusivity.  In  dynamical  units  H  becomes  ML2T~2,  and  the  formula  changes  to 
MLT"8®-1.  The  conversion  factors  obtained  from  these  are  Pt~l  and  m!rs6~l 
respectively. 

Similarly  for  emission  and  absorption  we  have  — 

4.  Emissivity  and  Immissivity.  —  These  are  the  quantities  of  heat  given 
off  by  or  taken  in  by  the  body  per  unit  of  time  per  unit  of  surface  per  unit  dif- 
ference of  temperature  between  the  surface  and  the  surrounding  medium.  We 
thus  get  the  equation 


The  dimensional  formula  for  E  is  therefore  ML~2T"J,  and  the  conversion  factor 


XXIV  INTRODUCTION. 


ml~'it~l.     In  thermometric  units  by  substituting  /8  for  m  the  factor  becomes  lt~\ 
and  in  dynamical  units 


5.  Thermal  Capacity.  —  This  is  the  product  of  the  number  for  mass  and 
the   specific  heat,  and  hence  the  dimensional  formula  and  conversion  factor  are 
.simply  M  and  m. 

6.  Latent  Heat.  —  Latent  heat  is  the  ratio  of  the  number  representing  the 
•quantity  of  heat  required  to  change  the  state  of  a  body  to  the  number  represent- 
ing the  quantity  of  matter  in   the  body.     The  dimensional  formula  is  therefore 
Mfe'/M  or  ®,  and  hence  the  conversion  factor  is  simply  the  ratio  of  the  tempera- 
ture units  or  0.     In  dynamical  units  the  factor  is  T2/"2.* 

7.  Joule's    Equivalent.  —  Joule's  dynamical  equivalent  is  connected  with 
quantity  of  heat  by  the  equation 

ML2T-2  =  JH  or  JM0. 

This  gives  for  the  dimensional  formula  of  J  the  expression  UT~2®~1.  The  conver- 
sion factor  is  thus  represented  by  f2f~*Q~l.  When  heat  is  measured  in  dynamical 
units  J  is  a  simple  number. 

8.  Entropy.  —  The  entropy  of  a  body  is  directly  proportional  to  the  quantity 
of  heat  it  contains  and  inversely  proportional  to  its  temperature.     The  dimen- 
sional formula  is  thus  M®/®  or  M,  and  the  conversion  factor  is  m.    When  heat  is 
measured  in  dynamical  units  the  factor  is  flz/2/"2^""1. 

Examples,  (a)  Find  the  relation  between  the  British  thermal  unit,  the  calorie, 
and  the  therm. 

Neglecting  the  variation  of  the  specific  heat  of  water  with  temperature,  or  de- 
fining all  the  units  for  the  same  temperature  of  the  standard  substance,  we  have 
the  following  definitions.  The  British  thermal  unit  is  the  quantity  of  heat  required 
to  raise  the  temperature  of  one  pound  of  water  i°  F.  The  calorie  is  the  quan- 
tity of  heat  required  to  raise  the  temperature  of  one  kilogramme  of  water  i°  C. 
The  therm  is  the  quantity  of  heat  required  to  raise  the  temperature  of  one  gramme 
of  water  i°  C.  Hence  :  — 

(1)  To  find  the   number  of   calories    in    one    British   thermal  unit,   we  have 

^  =  •45399  and  G  =  $  '>  •'•  »*0  =-45399  X  5/9  =  -25199. 

(2)  To   find   the    number   of   therms   in   one   calorie,  m=iooo   and    0=i; 
.-.  mO=.  1000. 

It  follows  at  once  that  the  number  of  therms  in  one  British  thermal  unit  is 
1000  X  .25199  =  251.99. 

(b)  What  is  the  relation  between  the  foot  grain  second  Fahrenheit-degree  and 
the  centimetre  gramme  second  Centigrade-degree  units  of  conductivity  ? 

The  number  of  the   latter  units  in  one  of  the  former  is  given  by  the  for- 

*  It  will  be  noticed  that  when  ©  is  given  the  dimension  formula  L2T~  2  the  formulae  in  thermal 
and  dynamical  units  are  always  identical.  The  thermometric  units  practically  suppress  mass. 


INTRODUCTION.  XXV 

mula  ml~lt~lb°,  where  m  =  .  064  799,  1=  30.48,  and  /=  i,  and  is  therefore  = 
.064799/30.48=:  2.126  X  io~3. 

(c)  Find  the  relation  between  the  units  stated  in  (b)  for  emissivity. 

In  this  case  the  conversion  formula  is  ml~*t~l,  where  ml  and  /  have  the 
same  value  as  before.  Hence  the  number  of  the  latter  units  in  the  former  is 
0.064  799/30.48'2  —  6.975  X  io~5. 

(d)  Find  the  number  of  centimetre  gramme  second  units  in  the  inch  grain 
hour  unit  of  emissivity. 

Here  the  formula  is  w/~2/-1,  where  #2  =  0.064799,  ^—  2-54>  ar>d  /  =  36oo. 
Therefore  the  required  number  is  0.064  799/2.  542  X  3600  =  2.790  X  io~6. 

(e)  If  Joule's  equivalent  be  776  foot  pounds  per  pound  of  water  per  degree 
Fahrenheit,  what  will  be  its  value  in  gravitation  units  when  the  metre,  the 
kilogramme,  and  the  degree  Centigrade  are  units  ? 


The  conversion  factor  in  this  case  is  ,,_2  or  16  \  where  /  =  .3048  and 
0-l  =  i.S;  .'.  776  X  .3048  X  1.8=425.7. 

(/")  If  Joule's  equivalent  be  24832  foot  poundals  when  the  degree  Fahren- 
heit is  unit  of  temperature,  what  will  be  its  value  when  kilogramme  metre 
second  and  degree-Centigrade  units  are  used  ? 

The  conversion  factor  is  llt~~0~l,  where  /=  .3048,  /  =  i,  and  0~l  =  1.8  ; 

.;.  24832  x  rr'2o~l  =  24832  x  .3048*  x  1.8  =  4152.5. 

In  gravitation  units  this  would  give  4152.5/9.81  =423.3. 


ELECTRIC   AND   MAGNETIC   UNITS. 

There  are  two  systems  of  these  units,  the  electrostatic  and  the  electromagnetic 
systems,  which  differ  from  each  other  because  of  the  different  fundamental  suppo- 
sitions on  which  they  are  based.  In  the  electrostatic  system  the  repulsive  force 
between  two  quantities  of  static  electricity  is  made  the  basis.  This  connects  force, 

quantity  of  electricity,  and  length  by  the  equation  f=a  ^,where  /  is  force,  a  a 

quantity  depending  on  the  units  employed  and  on  the  nature  of  the  medium,  q  and 
qt  quantities  of  electricity,  and  /  the  distance  between  q  and  qr  The  magnitude  of 
the  force  /  for  any  particular  values  of  q,  qt  and  /  depends  on  a  property  of  the 
medium  across  which  the  force  takes  place  called  its  inductive  capacity.  The  in- 
ductive capacity  of  air  has  generally  been  assumed  as  unity,  and  the  inductive 
capacity  of  other  media  expressed  as  a  number  representing  the  ratio  of  the  induc- 
tive capacity  of  the  medium  to  that  of  air.  These  numbers  are  known  as  the  spe- 
cific inductive  capacities  of  the  media.  According  to  the  ordinary  assumption, 
then,  of  air  as  the  standard  medium,  we  obtain  unit  quantity  of  electricity  when 
in  the  above  equation  q  —  q,,  and/,  0,  and  /  are  each  unity.  A  formal  definition 
is  given  below. 

In  the  electromagnetic  system  the  repulsion  between  two  magnetic  rjoles  or 


XXVI  INTRODUCTION. 

quantities  of  magnetism  is  taken  as  the  basis.  In  this  system  the  quantities  force, 
quantity  of  magnetism,  and  length  are  connected  by  an  equation  of  the  form 

/=*^ 

where  m  and  mt  are  in  this  case  quantities  of  magnetism,  and  the  other  symbols 
have  the  same  meaning  as  before.  In  this  case  it  has  been  usual  to  assume  the 
magnetic  inductive  capacity  of  air  to  be  unity,  and  to  express  the  magnetic  induc- 
tive capacity  of  other  media  as  a  simple  number  representing  the  ratio  of  the  in- 
ductive capacity  of  the  medium  to  that  of  air.  These  numbers,  by  analogy  with 
specific  inductive  capacity  for  electricity,  might  be  called  specific  inductive  capac- 
ities for  magnetism.  They  are  usually  called  permeabilities.  (Vide  Thomson, 
"  Papers  on  Electrostatics  and  Magnetism,"  p.  484.)  In  this  case,  also,  like  that 
for  electricity,  the  unit  quantity  of  magnetism  is  obtained  by  making  m  =  mt)  and 
fj  a,  and  /  each  unity. 

In  both  these  cases  the  intrinsic  inductive  capacity  of  the  standard  medium  is- 
suppressed,  and  hence  also  that  of  all  other  media.  Whether  this  be  done  or  not, 
direct  experiment  has  to  be  resorted  to  for  the  determination  of  the  absolute  val- 
ues of  the  units  and  the  relations  of  the  units  in  the  one  system  to  those  in  the 
other.  'The  character  of  this  relation  can  be  directly  inferred  from  the  dimen- 
sional formulae  of  the  different  quantities,  but  these  can  give  no  information  as  to 
the  relative  absolute  values  of  the  units  in  the  two  systems.  Prof.  Riicker  has 
suggested  (Phil.  Mag.  vol.  27)  the  advisability  of  at  least  indicating  the  exist- 
ence of  the  suppressed  properties  by  putting  symbols  for  them  in  the  dimensional 
formulae.  This  has  the  advantage  of  showing  how  the  magnitudes  of  the  different 
units  would  be  affected  by  a  change  in  the  standard  medium,  or  by  making  the 
standard  medium  different  for  the  two  systems.  In  accordance  with  this  idea,  the 
symbols  K  and  P  have  been  introduced  into  the  formulae  given  below  to  represent 
inductive  capacity  in  the  electrostatic  and  the  electromagnetic  systems  respectively. 
In  the  conversion  formulae  k  and/  are  the  ordinary  specific  inductive  capacities 
and  permeabilities  of  the  media  when  air  is  taken  as  the  standard,  or  generally 
those  with  reference  to  the  first  medium  taken  as  standard.  The  ordinary  for- 
mulae may  be  obtained  by  putting  K  and  P  equal  to  unity. 


ELECTROSTATIC   UNITS. 

i.  Quantity  of  Electricity.  —  The  unit  quantity  of  electricity  is  defined  as 
that  quantity  which  if  concentrated  at  a  point  and  placed  at  unit  distance  from  an 
equal  and  similarly  concentrated  quantity  repels  it,  or  is  repelled  by  it,  with  unit 
force.  The  medium  or  dielectric  is  usually  taken  as  air,  and  the  other  units  in  ac- 
cordance with  the  centimetre  gramme  second  system. 

In  this  case  we  have  the  force  of  repulsion  proportional  directly  to  the  square 
of  the  quantity  of  electricity  and  inversely  to  the  square  of  the  distance  between 
the  quantities  and  to  the  inductive  capacity.  The  dimensional  formula  is  there- 
fore the  same  as  that  for  [force  X  length2  X  inductive  capacity]*  or 
and  the  conversion  factor  is 


INTRODUCTION.  XXV1L 

2.  Electric  Surface  Density  and  Electric  Displacement.  —  The  density 
of  an  electric  distribution  at  any  point  on  a  surface  is  measured  by  the  quantity 
per  unit  of  area,  and  the  electric  displacement  at  any  point  in  a  dielectric  is  mea- 
sured by  the  quantity  displaced  per  unit  of  area.    These  quantities  have  therefore 
the  same  dimensional  formula,  namely,  the  ratio  of  the  formulae  for  quantity  of 
electricity  and  for  area  or  M^I/^T^K*,  and  the  conversion  factor  m*l~^t~l&. 

3.  Electric  Force  at  a  Point,  or  Intensity  of  Electric  Field.  —  This  is 
measured  by  the  ratio  of  the  magnitude  of  the  force  on  a  quantity  of  electricity  at 
a  point  to  the  magnitude  of  the  quantity  of  electricity.     The  dimensional  formula. 
is  therefore  the  ratio  of  the  formulae  for  force  and  electric  quantity,  or 


which  gives  the  conversion  factor  m*l~l-t~lk~*-. 

4.  Electric  Potential  and  Electromotive  Force.  —  Change  of  potential 
is  proportional  to  the  work  done  per  unit  of  electricity  in  producing  the  change. 
The  dimensional  formula  is  therefore  the  ratio  of  the  formulae  for  work  and  elec- 
tric quantity,  or 

ML2T~-     —  M*LiT~1K~l 


which  gives  the  conversion  factor 

5.  Capacity  of  a  Conductor.  —  The  capacity  of  an  insulated  conductor  is 
proportional  to  the  ratio  of  the  numbers  representing  the  quantity  of  electricity  in 
a  charge  and  trie  potential  of  the  charge.  The  dimensional  formula  is  thus  the 
ratio  of  the  two  formulae  for  electric  quantity  and  potential,  or 


LK 

K-i 

which  gives  Ik  for  conversion  factor.    When  K  is  taken  as  unity,  as  in  the  ordinary 
units,  the  capacity  of  an  insulated  conductor  is  simply  a  length. 

6.  Specific  Inductive  Capacity.  —  This  is  the  ratio  of  the  inductive  capac- 
ity of  the  substance  to  that  of  a  standard  substance,  and  hence  the  dimensional 
formula  is  K/K  or  i.* 

' 

7.  Electric  Current.  —  Current  is  quantity  flowing  past  a  point  per  unit  of 
time.     The  dimensional  formula  is  thus  the  ratio  of  the  formulae  for  electric  quan- 
tity and  for  time,  or 


and  the  conversion  factor 

*  According  to  the  ordinary  definition  referred  to  air  as  standard  medium,  the  specific  inductive 
capacity  of  a  substance  is  K,  or  is  identical  in  dimensions  with  what  is  here  taken  as  inductive  ca- 
pacity. Hence  in  that  case  the  conversion  factor  must  be  taken  as  I  on  the  electrostatic  and  as 
the  electromagnetic  system. 


XXVlli  INTRODUCTION. 

8.  Conductivity,  or  Specific*  Conductance.  —  This,  like  the  corresponding 
term  for  heat,  is  quantity  per  unit  area  per  unit  potential  gradient  per  unit  of  time. 
The  dimensional  formula  is  therefore 

electric  quantity 


g  area  X  potential  gradient  X  time 

T7~ 
The  conversion  factor  is  t~lk. 

9.  Specific  *  Resistance.  —  This  is  the  reciprocal  of  conductivity  as  above 
defined,  and  hence  the  dimensional  formula  and  conversion  factor  are  respec- 
tively TK"1  and  tk~l. 

10.  Conductance.  —  The  conductance  of  any  part  of  an  electric  circuit,  not 
containing  a  source  of  electromotive  force,  is  the  ratio  of  the  numbers  represent- 
ing the  current  flowing  through  it  and  the  difference  of  potential  between  its  ends. 
The  dimensional  formula  is  thus  the  ratio  of  the  formulae  for  current  and  poten- 
tial, or 


from  which  we  get  the  conversion  factor  lr*k. 

1  1  .   Resistance.  —  This  is  the  reciprocal  of  conductance,  and  therefore  the 
dimensional  formula  and  the  conversion  factor  are  respectively  I/^TK""1  and 

rv/r1. 


EXAMPLES    OF    CONVERSION    IN    ELECTROSTATIC    UNITS. 

(a)  Pind  the  factor  for  converting  quantity  of  electricity  expressed  in  foot  grain 
second  units  to  the  same  expressed  in  c.  g.  s.  units. 

By  (i)  the  formula  is  w1/8/"1^,  in  which  in  this  case  m  =  0.0648,  /=  30.48,  /  = 
i,  and  k  =  i  ;  .*.  the  factor  is  0.0648*  X  30.48*  =  4.2836. 

(b)  Find  the  factor  required  to  convert  electric  potential  from  millimetre  milli- 
gramme second  units  to  c.  g.  s.  units. 

By  (4)  the  formula  is  wV-/"1^"-,  and  in  this  case  m  =  o.ooi,  /=  o.i,  /=  i,  and 
£=i;  .*.  the  factor  =  o.ooi*  X  o.i}  =  o. 01. 

(c)  Find  the  factor  required  to  convert  from  foot  grain  second  and  specific  in- 
ductive capacity  6  units  to  c.  g.  s.  units. 

By  (5)  the  formula  is  //£,  and  in  this  case  /=30.48  and  £  =  6;  .'.  the  factor 
=  30.48  X  6=182.88. 

*  The  term  "  specific/'  as  used  here  and  in  9,  refers  conductance  and  resistance  to  that  between 
the  ends  of  a  bar  of  unit  section  and  unit  length,  and  hence  is  different  from  the  same  term  in 
specific  heat,  specific  inductivity,  capacity,  etc.,  which  refer  to  a  standard  substance. 


INTRODUCTION.  XXIX 


ELECTROMAGNETIC   UNITS. 

As  stated  above,  these  units  bear  the  same  relation  to  unit  quantity  of  magne- 
tism that  the  electric  units  do  to  quantity  of  electricity.  Thus,  when  inductive 
capacity  is  suppressed,  the  dimensional  formula  for  magnetic  quantity  on  this  sys- 
tem is  the  same  as  that  for  electric  quantity  on  the  electrostatic  system.  All  quan- 
tities in  this  system  which  only  differ  from  corresponding  quantities  defined  above 
by  the  substitution  of  magnetic  for  electric  quantity  may  have  their  dimensional 
formulae  derived  from  those  of  the  corresponding  quantity  by  substituting  P 
for  K. 

1.  Magnetic  Pole,  or  Quantity  of  Magnetism.  —  Two  unit  quantities  of 
magnetism  concentrated  at  points  unit  distance  apart  repel  each  other  with  unit 
force.     The  dimensional  formula  is  thus  the  same   as  for  [force  X  length2  X  in- 
ductive capacity]  or  M^UT"1?*,  and  the  conversion  factor  is  wW"1/*. 

2.  Density  of  Surface  Distribution  of  Magnetism.  —  This  is  measured 
by  quantity  of  magnetism  per  unit  area,  and  the  dimension  formula  is  therefore 
the  ratio  of  the  expressions  for  magnetic  quantity  and  for  area,  or 

which  gives  the  conversion  factor 


3.  Magnetic  Force  at  a  Point,  or  Intensity  of  Magnetic  Field.  —  The 

number  for  this  is  the  ratio  of  the  numbers  representing  the  magnitudes  of  the 
force  on  a  magnetic  pole  placed  at  the  point  and  the  magnitude  of  the  magnetic 
pole. 

The  dimensional  formula  is  therefore  the  ratio  of  the  expressions  for  force  and 
magnetic  quantity,  or 


and  the  conversion  factor  mtl~*t~lp~*. 

4.  Magnetic  Potential.  —  The  magnetic  potential  at  a  point  is  measured  by 
the  work  which  is  required  to  bring  unit  quantity  of  positive  magnetism  from  zero 
potential  to  the  point.  The  dimensional  formula  is  thus  the  ratio  of  the  formula 
for  work  and  magnetic  quantity,  or 


which  gives  the  conversion  factor 

5.  Magnetic    Moment.  —  This   is   the   product   of  the   numbers  for  pole 
strength  and  length  of  a  magnet.     The  dimensional  formula  is  therefore  the  pro- 
duct of  the  formulae  for  magnetic  quantity  and  length,  or  M^UT"1?1,  and  the  con- 
version factor  in*-fit~lp}l. 

6.  Intensity  of  Magnetization.  —  The  intensity  of  magnetization  of  any  por- 
tion of  a  magnetized  body  is  the  ratio  of  the  numbers  representing  the  magni- 


;XXX  INTRODUCTION. 


tude  of  the  magnetic  moment  of  that  portion  and  its  volume.     The  dimensional 
formula  is  therefore  the  ratio  of  the  formulae  for  magnetic  moment  and  volume,  or 


JL* 

The  conversion  factor  is  therefore 

7.  Magnetic  Permeability,*  or  Specific  Magnetic  Inductive  Capacity. 

-  This  is  the  analogue  in  magnetism  to  specific  inductive  capacity  in  electricity. 
It  is  the  ratio  of  the  magnetic  induction  in  the  substance  to  the  magnetic  induc- 
tion in  the  field  which  produces  the  magnetization,  and  therefore  its  dimensional 
formula  and  conversion  factor  are  unity. 

8.  Magnetic  Susceptibility.  —  This  is  the  ratio  of  the  numbers  which  repre- 
.sent  the  values  of  the  intensity  of  magnetization  produced  and  the  intensity  of  the 
magnetic  field  producing  it.     The  dimensional  formula  is  therefore  the  ratio  of 
the  formulae  for  intensity  of  magnetization  and  magnetic  field  or 


The  conversion  factor  is  therefore/,  and  both  the  dimensional  formula  and  con- 
version factor  are  unity  in  the  ordinary  system. 

9.  Current  Strength.  —  A  current  of  strength  c  flowing  round  a  circle  of 
radius  r  produces  a  magnetic  field  at  the  centre  of  intensity  27r<r/r.     The  dimen- 
sional formula  is  therefore  the  product  of  the  formulae  for  magnetic  field  intensity 
and  length,  or  M-L^T"1?"*,  which  gives  the  conversion  factor  wV-/"1/"*. 

10.  Current  Density,  or  Strength  of  Current  at  a  Point.  —  This  is  the 
ratio  of  the  numbers  for  current  strength  and  area.     The  dimensional  formula 
and  the  conversion  factor  are  therefore  M^Lr^T"1?"^  and 


11.  Quantity  of  Electricity.  —  This  is  the  product  of  the  numbers  for  cur- 
rent and  time.    The  dimensional  formula  is  therefore  M^T"1?"*  X  T=  MJL*P-*, 
and  the  conversion  factor  mWp~*. 

12.  Electric  Potential,  or  Electromotive  Force.  —  As  in  the  electrostatic 
system,  this  is  the  ratio  of  the  numbers  for  work  and  quantity  of  electricity.     The 
•dimensional  formula  is  therefore 

ML2T~2 


and  the  conversion  factor 

*  Permeability,  as  ordinarily  taken  with  the  standard  medium  as  unity,  has  the  same  dimension 
formula  and  conversion  factor  as  that  which  is  here  taken  as  magnetic  inductive  capacity.  Hence 
for  ordinary  transformations  the  conversion  factor  should  be  taken  as  I  in  the  electromagnetic  and 
in  the  electrostatic  systems. 


INTRODUCTION.  XXXI 


13.  Electrostatic  Capacity.  —  This  is  the  ratio  of  the  numbers  for  quantity 
of  electricity  and  difference  of  potential.     The  dimensional  formula  is  therefore 


.and  the  conversion  factor  /~1/^~1. 

14.  Resistance  of  a  Conductor.  —  The  resistance  of  a  conductor  or  elec- 
trode is  the  ratio  of  the  numbers  for  difference  of  potential  between  its  ends  and 
the  constant  current  it  is  capable  of  producing.     The  dimensional  formula  is 
therefore  the  ratio  of  those  for  potential  and  current  or 

-!-"  __  T  T_lp 
pR 

The  conversion  factor  thus  becomes  lt~lp,  and  in  the  ordinary  system  resistance 
has  the  same  conversion  factor  as  velocity. 

15.  Conductance.  —  This  is  the  reciprocal  of  resistance,  and  hence  the  dimen- 
sional formula  and  conversion  factor  are  respectively  L"1  TP"1  and  l~ltp~l. 

16.  Conductivity,  or  Specific  Conductance.  —  This  is  quantity  of  electric- 
ity transmitted  per  unit  of  area  per  unit  of  potential  gradient  per  unit  of  time. 
The  dimensional  formula  is  therefore  derived  from  those  of  the  quantities  men- 
tioned as  follows:  — 

~ 

_  _  T  -2-rp-l 

-"^ 


The  conversion  factor  is  therefore  /~2^~1. 

17.  Specific  Resistance.  —  This  is  the  reciprocal  of  conductivity  as  defined 
in  15,  and  hence  the  dimensional  formula  and  conversion  factor  are  respectively 
and 


18.  Coefficient  of  Self-induction,  or  Inductance,  or  Electro-kinetic  In- 
ertia. —  These  are  for  any  circuit  the  electromotive  force  produced  in  it  by  unit 
rate  of  variation  of  the  current  through  it.  The  dimensional  formula  is  therefore 
the  product  of  the  formulae  for  electromotive  force  and  time  divided  by  that  for 
current  or 


The  conversion  factor  is  therefore  lp,  and  in  the  ordinary  system  is  the  same  as 
that  for  length. 

. 

19.  Coefficient  of  Mutual  Induction. — The  mutual  induction  of  two  cir- 
cuits is  the  electromotive  force  produced  in  one  per  unit  rate  of  variation  of  the 
current  in  the  other.  The  dimensional  formula  and  the  conversion  factor  are 
therefore  the  same  as  those  for  self-induction. 


XXX11  INTRODUCTION. 

20.  Electro-kinetic  Momentum.  —  The  number  for  this  is  the  product  of 
the  numbers  for  current  and  for  electro-kinetic  inertia.  The  dimensional  formula 
is  therefore  the  product  of  the  formulas  for  these  quantities,  or  M^UT"1?"*  X  LP 
and  the  conversion  factor  is 


21.  Electromotive  Force  at  a  Point.  —  The  number  for  this  quantity  is 
the  ratio  of  the  numbers  for  electric  potential  or  electromotive  force  as  given  in 
12,  and  for  length.     The  dimensional  formula  is  therefore  M*L*T~2P4,  and  the 
conversion  factor  m<l'-t~-p}i. 

22.  Vector  Potential.  —  This  is  time  integral  of  electromotive  force  at  n 
point,  or  the  electro-kinetic  momentum  at  a  point.     The  dimensional  formula 
may  therefore  be  derived  from  21  by  multiplying  by  T,  or  from  20  by  dividing 
by  L.     It  is  therefore  MWT"1?*,  and  the  conversion  factor  w'/V"1/*. 

23.  Thermoelectric  Height.  —  This  is  measured  by  the  ratio  of  the  num- 
bers for  electromotive  force  and  for  temperature.     The  dimensional  formula  is 
therefore  the  ratio  of  the  formulae  for  these  two  quantities,  or  M'L?T~2P-©-1,  and 
the  conversion  factor 


24.  Specific  Heat  of  Electricity.  —  This  quantity  is  measured  in  the  same 
way  as  23,  and  hence  has  the  same  formulas. 

25.  Coefficient  of  Peltier  Effect.  —  This  is  measured  by  the  ratio  of  the 
numbers  for  quantity  of  heat  and  for  quantity  of  electricity.     The  dimensional 
formula  is  therefore 


and  the  conversion  factor  n 


EXAMPLES    OF    CONVERSION    IN    ELECTROMAGNETIC    UNITS. 

(a)  Find  the  factor  required  to  convert  intensity  of  magnetic  field  from  foot 
grain  minute  units  to  c.  g.  s.  units. 

By  (3)  the  formula  is  m*f~*r~lp-*,  and  in  this  case  m  =  0.0648,  1=  30.48,  t  — 
60,  and/  =  i  ;  .'.  the  factors  =  0.0648*  X  30.48"*  X  6o~1=  0.00076847. 

Similarly  to  convert  from  foot  grain  second  units  to  c.  g.  s.  units  the  factor  is 
0.0648*  X  30. 48~1-  =.  0.046  1 08. 

(b)  How  many  c.  g.  s.  units  of  magnetic  moment  make  one  foot  grain  second 
unit  of  the  same  quantity  ? 

By  (5)  the  formula  is  m*flf~lfl,  and  the  values  for  this  problem  are  m  —  0.0648, 
t=  30.48,  /=  i,  and/  =  i  ;  .'.  the  number  =  0.0648*  X  30-48*=  1305.6. 

(c)  If  the  intensity  of  magnetization  of  a  steel  bar  be  700  in  c.  g.  s.  units,  what 
will  it  be  in  millimetre  milligramme  second  units  ? 


INTRODUCTION.  XXX111 


By  (6)  the  formula  is  wV*/"1/*,  and  in  this  case  m  —  1000,  1  =  10,  /  =  i,  and 
p  =  i  ;  .'.  the  intensity  =  700  X  ioooj  X  io1  =  70000. 

(</)  Find  the  factor  required  to  convert  current  strength  from  c.  g.  s.  units  to 
earth  quadrant  io~n  gramme  and  second  units. 

By  (9)  the  formula  is  w*^/"1/"1,  and  the  values  of  these  quantities  are  here  m  — 
jo11,  /=  io~9,  /=  i,  and/  =  i  ;  /.  the  factor  =  10^  X  io~$  =  10. 

(e)  Find  the  factor  required  to  convert  resistance  expressed  in  c.  g.  s.  units  into 
the  same  expressed  in  earth-quadrant  io~n  grammes  and  second  units. 

By  (14)  the  formula  is  lt~^p,  and  for  this  case  /=  io~',  /=  i,  and  /  =  i  ; 
/.  the  factor  =  io~9. 

(/)  Find  the  factor  required  to  convert  electromotive  force  from  earth-quadrant 
io~~"  gramme  and  second  units  to  c.  g.  s.  units. 

By  (12)  the  formula  is  w*/1/"^*,  and  for  this  case  m  =  io~n,  /=  io9,  /=  i, 
and/  =  i  ;  /.the  factor  =  io8. 


PRACTICAL  UNITS. 

In  practical  electrical  measurements  the  units  adopted  are  either  multiples  or 
submultiples  of  the  units  founded  on  the  centimetre,  the  gramme,  and  the  second 
as  fundamental  units,  and  air  is  taken  as  the  standard  medium,  for  which  K  and  P 
are  assumed  unity.  The  following,  quoted  from  the  report  to  the  Honorable  the 
Secretary  of  State,  under  date  of  November  6th,  1893,  by  the  delegates  repre- 
senting the  United  States,  gives  the  ordinary  units  with  their  names  and  values 
as  defined  by  the  International  Congress  at  Chicago  in  1893  :  — 

"  Resolved.  That  the  several  governments  represented  by  the  delegates  of  this 
International  Congress  of  Electricians  be,  and  they  are  hereby,  recommended  to 
formally  adopt  as  legal  units  of  electrical  measure  the  following :  As  a  unit  of  re- 
sistance, the  international  ohm,  which  is  based  upon  the  ohm  equal  to  io9  units  of 
resistance  of  the  C.  G.  S.  system  of  electro-magnetic  units,  and  is  represented 
by  the  resistance  offered  to  an  unvarying  electric  current  by  a  column  of  mercury 
at  the  temperature  of  melting  ice  14.4521  grammes  in  mass,  of  a  constant  cross- 
sectional  area  and  of  the  length  of  106.3  centimetres. 

"  As  a  unit  of  current,  the  international  ampere,  which  is  one  tenth  of  the  unit  of 
current  of  the  C.  G.  S.  system  of  electro-magnetic  units,  and  which  is  represented 
sufficiently  well  for  practical  use  by  the  unvarying  current  which,  when  passed 
through  a  solution  of  nitrate  of  silver  in  water,  and  in  accordance  with  accom- 
panying specifications,1*  deposits  silver  at  the  rate  of  0.001118  of  a  gramme  per 
second. 

*  "  In  the  following  specification  the  term  '  silver  voltameter '  means  the  arrangement  of  appara- 
tus by  means  of  which  an  electric  current  is  passed  through  a  solution  of  nitrate  of  silver  in  water. 
The  silver  voltameter  measures  the  total  electrical  quantity  which  has  passed  during  the  time  of 
the  experiment,  and  by  noting  this  time  the  time  average  of  the  current,  or,  if  the  current  has  been 
kept  constant,  the  current  itself  can  be  deduced. 

"  In  employing  the  silver  voltameter  to  measure  currents  of  about  one  ampere,  the  following 
arrangements  should  be  adopted  :  — 


XXXIV  INTRODUCTION. 

"  As  a  unit  of  electromotive  force,  the  international  volt,  which  is  the  electro- 
motive force  that,  steadily  applied  to  a  conductor  whose  resistance  is  one  interna- 
tional ohm,  will  produce  a  current  of  one  international  ampere,  and  which  is  rep- 
resented sufficiently  well  for  practical  use  by  y^§£  of  the  electromotive  force 
between  the  poles  or  electrodes  of  the  voltaic  cell  known  as  Clark's  cell,  at  a  tem- 
perature of  15°  C.,  and  prepared  in  the  manner  described  in  the  accompanying 
specification.* 

"  As  a  unit  of  quantity,  the  international  coulomb,  which  is  the  quantity  of  elec- 
tricity transferred  by  a  current  of  one  international  ampere  in  one  second. 

'•  As  a  unit  of  capacity,  the  international  farad,  which  is  the  capacity  of  a  con- 
denser charged  to  a  potential  of  one  international  volt  by  one  international  cou- 
lomb of  electricity. t 

"  As  a  unit  of  work,  the  joule,  which  is  equal  to  io7  units  of  work  in  the  c.  g.  s. 
system,  and  which  is  represented  sufficiently  well  for  practical  use  by  the  energy 
expended  in  one  second  by  an  international  ampere  in  an  international  ohm. 

"  As  a  unit  of  power,  the  watt,  which  is  equal  to  io7  units  of  power  in  the  c.  g.  s. 
system,  and  which  is  represented  sufficiently  well  for  practical  use  by  the  work 
done  at  the  rate  of  one  joule  per  second. 

"  As  the  unit  of  induction,  the  henry,  which  is  the  induction  in  a  circuit  when 
the  electromotive  force  induced  in  this  circuit  is  one  international  volt,  while  the 
inducing  current  varies  at  the  rate  of  one  ampere  per  second. 

"The  Chamber  also  voted  that  it^was  not  wise  to  adopt  or  recommend  a  stand- 
ard of  light  at  the  present  time." 

By  an  Act  of  Congress  approved  July  i2th,  1894,  the  units  recommended  by 
the  Chicago  Congress  were  adopted  in  this  country  with  only  some  unimportant 
verbal  changes  in  the  definitions. 

By  an  Order  in  Council  of  date  August  23d,  1894,  the  British  Board  of  Trade 
adopted  the  ohm,  the  ampere,  and  the  volt,  substantially  as  recommended  by 
the  Chicago  Congress.  The  other  units  were  not  legalized  in  Great  Britain. 
They  are,  however,  in  general  use  in  that  country  and  all  over  the  world. 

"  The  kathode  on  which  the  silver  is  to  be  deposited  should  take  the  form  of  a  platinum  bowl 
not  less  than  io  centimetres  in  diameter  and  from  4  to  5  centimetres  in  depth. 

"The  anode  should  be  a  plate  of  pure  silver  some  30  square  centimetres  in  area  and  2  or  3 
millimetres  in  thickness. 

"This  is  supported  horizontally  in  the  liquid  near  the  top  of  the  solution  by  a  platinum  wire 
passed  through  holes  in  the  plate  at  opposite  corners.  To  prevent  the  disintegrated  silver  which 
is  formed  on  the  anode  from  falling  on  to  the  kathode,  the  anode  should  be  wrapped  round  with 
pure  filter  paper,  secured  at  the  back  with  sealing  wax. 

"The  liquid  should  consist  of  a  neutral  solution  of  pure  silver  nitrate,  containing  about  15  parts 
by  weight  of  the  nitrate  to  85  parts  of  water. 

"The  resistance  of  the  voltameter  changes  somewhat  as  the  current  passes.  To  prevent  these 
changes  having  too  great  an  effect  on  the  current,  some  resistance  besides  that  of  the  voltameter 
should  be  inserted  in  the  circuit.  The  total  metallic  resistance  of  the  circuit  should  not  be  less 
than  io  ohms." 

*  "  A  committee,  consisting  of  Messrs.  Helmholtz,  Ayrton,  and  Carhart,  was  appointed  to  pre- 
pare specifications  for  the  Clark's  cell.  Their  report  has  not  yet  been  received." 

•f  The  one  millionth  part  of  the  farad  is  more  commonly  used  in  practical  measurements,  and  is 
called  the  microfarad. 


PHYSICAL   TABLES 


TABLE  1 . 


FUNDAMENTAL  AND  DERIVED  UNITS. 


(a)  FUNDAMENTAL  UNITS. 

Name  of  Unit.                                           Symbol. 

Conversion  Factor. 

Length.                                                                           L 
Mass.                                                                              M 

m 

Time.                                                                              T 

t 

Temperature.                                                                 ® 
Electric  Inductive  Capacity.                                        K 
Magnetic  Inductive  Capacity.                                      P 

0 
k 
P 

(&)  DERIVED  UNITS. 

/.    Geometric  and  Dynamic  Units. 

Name  of  Unit. 

Conversion  Factor. 

Area. 

1         /2 

Volume. 
Angle. 
Solid  Angle. 
Curvature. 

\ 
I 

I 

Tortuosity. 
Specific  curvature  of  a  surface. 
Angular  velocity. 
Angular  acceleration. 
Linear  velocity. 
Linear  acceleration. 
Density. 
Moment  of  inertia. 

r1 
/r2 

ir2 

ml2 

Intensity  of  attraction,  or  "  force  at  a  point." 
Absolute  force  of  a  centre  of  attraction,  or  "  strength  | 
of  a  centre."                                                                    ) 

ir2 

Momentum. 

mir1 

Moment  of  momentum,  or  angular  momentum. 
Force. 

m  I2  r1 

mir* 

Moment  of  a  couple,  or  torque. 
Intensity  of  stress. 
Modulus  of  elasticity. 
Work  and  energy. 
Resilience. 

m  I2  f~2 
m  t~l  r2 

m  /-1  r2 

m  I2  r2 

m  /-1  r2 

Power  or  activity. 

m  I2  t~z 

SMITHSONIAN  TABLES. 


FUNDAMENTAL  AND  DERIVED   UNITS. 


TABLE  1 


//.    Heat  Units. 


Name  of  Unit. 


Conversion  Factor. 


Quantity  of  heat  (thermal  units). 

"  "     (thermometric  units). 

"  "     (dynamical  units). 

Coefficient  of  thermal  expansion. 
Conductivity  (thermal  units). 

"  (thermometric  units),  or  diffusivity. 

"  (dynamical  units). 

Emissivity  and  imissivity  (thermal  units). 

"  "  (thermometric  units). 

"  "  (dynamical  units). 

Thermal  capacity. 
Latent  heat  (thermal  units). 

"         "     (dynamical  units). 
Joule's  equivalent. 

Entropy  (heat  measured  in  thermal  units). 
"          (  "  "  dynamical  units). 


m  0 


m 


m  t~B  6~l 
m 

e 

/2  r2  &-1 

m 

m  /2  r2  e-1 


///.   Magnetic  and  Electric  Units. 


Name  of  Unit. 


Conversion  factor 
for  electrostatic 
system. 


Conversion  factor 
for  electromag- 
netic system. 


" 


Magnetic  pole,  or  quantity  of  mag- 
netism. 

Density  of   surface   distribution 
magnetism. 

Intensity  of  magnetic  field. 

Magnetic  potential. 

Magnetic  moment. 

Intensity  of  magnetisation. 

Magnetic  permeability. 

Magnetic   susceptibility   and 

netic  inductive  capacity.  } 

Quantity  of  electricity. 

Electric  surface  density  and  electric  ) 


mag- 


displacement. 
Intensity  of  electric  field. 
Electric  potential  and  e.  m.  f. 
Capacity  of  a  condenser. 
Inductive  capacity. 
Specific  inductive  capacity. 
Electric  current. 


«»  f~*  k~+ 

m*flr*# 
nt  /•  r2  & 
m*  P  £-» 
m*  I*  k~i 

i 

/—  2  ^2  y£— 1 

m*  /J  r1  & 


m*  , 

Ik 

k 

i 


/-* 


/»/- 


1      ,3      ,      fl 

m*  r  t  *jr 
l~l  t*p~l 
I-2  /2/-1 
i 
*»/I/~VH 


SMITHSONIAN  TABLES. 


TABLE  1 . 


FUNDAMENTAL  AND   DERIVED  UNITS. 


///.    Magnetic  and  Electric  Units. 

Name  of  Unit. 

Conversion  factor 
for  electrostatic 
system. 

Conversion  factor 
for   electromag- 
netic system. 

Conductivity. 
Specific  resistance. 
Conductance. 

lt~l  k 

/«/-*/ 

Resistance. 
Coefficient   of   self    induction    and  \ 
coefficient  of  mutual  induction.      j 

^  7~-i 

irlp 
ip 

Electrokinetic  momentum. 

ml  /J  fe-\ 

ml  /'  t~l  p* 

Electromotive  force  at  a  point. 
Vector  potential. 
Thermoelectric  height  and  specific) 
heat  of  electricity.                             j 
Coefficient  of  Peltier  effect. 

nfi  l~*  t~*  k~^ 
m*  /-?  /  £-»  0 

m*  J-  t~2  p1* 

SMITHSONIAN  TABLES. 


TABLE  2. 

EQUIVALENTS    OF   METRIC    AND    BRITISH    IMPERIAL    WEIGHTS 
AND    MEASURES.* 

(I)    METRIC  TO   IMPERIAL. 


LINEAR  MEASURE. 

MEASURE   OF   CAPACITY. 

r  millimetre  (mm.)  I             0.03937    in. 

i  millilitre  (ml.)  (.001  )                 ~           ,     . 

(.001  m.)               ) 

litre)                         J  ~      ao610  C^b'  m- 

r  centimetre  (.01  m.)  =       °-3937o     ' 
i  decimetre  (.1  m.)   =       3-937OI 

i  centilitre  (.01  litre)      =  \  °-6lO24  "      " 

(  39-3/OII3  " 

)  0.070  gill. 

I   METRE  (m.)        .      -  =]      3.28o8d3  ft. 

(     1.0936143  yds. 

i  decilitre  (.1  litre)  .     .  =    0.176  pint. 

I    LITRE    (1,000    Cub.  ) 

i  dekametre  \                              /-             <t 

centimetres  or  i  >  =     1.75980  pints. 

(10  m.)      (     '     '           IO-93DI4 

cub.  decimetre)     ) 

(loom!)*  \   '    '  =    I09-36i43 

i  dekalitre  (10  litres)   .  =     2.200  gallons, 
i  hectolitre  (100  "    )    .  =     2.75  bushels. 

i  kilometre     I 
(i,ooom.)  J    '     '-       0.62137  mile. 

i  kilolitre  (1,000  "    )    .  =     3.437  quarters. 

i  myriametre   / 

(10,000  m.)  J  '                6.21372  miles. 

i  micron    .    .    .    .=       o.ooi  mm. 

APOTHECARIES'   MEASURE. 

SQUARE   MEASURE. 

i    cubic     centi-  )       C    0.03527  fluid  ounce, 
metre       fi>«J    0.28219  fluid  drachm, 
gramme  w't)  )       (  15.43235  grains  weight. 
I  cub.  millimetre  =      0.01693  minim. 

i  sq.  centimetre   .    .=       o.i55osq.  in. 

AVOIRDUPOIS  WEIGHT. 

i   sq.  decimetre         ) 

(100  sq.  centra.)  h       ^Soo  sq.  in. 

milligramme  (mgr.)      .  =    0.01543  grain. 

i  sq.  metre  or  centi-  f  (   10.7639  sq.  ft. 

centigramme  (.01  gram.)  =    0.15432      " 

arc  (loo  sq.  dcm.)  J       |     1.1960  sq.  yd. 

decigramme  (.1       "     )=     1.54324  grains. 

i  ARE  (loosq.  m.)       =    119.60  sq.  yds. 
I  hectare  (100  ares  ) 
or  10,000  sq.  m.)  J  ~        2.4711  acres. 

GRAMME       =    15.43235        " 

dekagramme  (10  gram.)  =     5.64383  drams, 
hectogramme  (  i  oo    "   )=     3.5273902. 
(  2.2046223  Ib. 

KILOGRAMME  (l,OOO  "   )  =  1  15432.3564 

(     grains. 

CUBIC   MEASURE. 

myriagramme(iokilog.)=  22.04621  Ib. 

quintal             (100  "     )  =     I  96841  cwt. 

i  cub.   centimetre      ) 

millier  or  tonne  )                    0.9842  ton. 
.(1,000  kilog.)    ) 

(c.c.)  (1,000  cubic  >  =   0.0610  cub.  in 

millimetres)             ) 

I  cub.  decimetre         ) 

TROY  WEIGHT. 

(c.d.)  (1,000  cubic  >  =61.024      "„      " 

centimetres)            ) 

C  0.03215  oz.  Troy. 

I   CUB.    METRE  )                 /                   _    »  ,      , 

orstere.     .5    =         35-3148  cVb   ft. 
(1,000  c.d.))                  1.307954  cub.  yd. 

i  GRAMME   .     .   ==  j  0.64301  penny  weight. 
*  :(l5-43236  grains. 

APOTHECARIES'  WEIGHT. 

(    0.25721  drachm. 

i  GRAMME    .     .    .     •  =  ]    0.77162  scruple. 

* 

(  r  5-43235  grains. 

NOTE.— The  METRE  is  the  length,  at*the  temperature  of  o°  C.,  of  the  platinum-iridium  bar  deposited 
with  the  Board  of  Trade. 

The  present  legal  equivalent  of  the  metre  is  39*370113  inches,  as  above  stated.  If  a  brass  ihetre  is, 
however,  compared,  not  at  its  legal  temperature  (o°  C.  or  32°F.)  but  at  the  temperature  of  62°  F.,  with  a 
brass  yard  at  the  temperature  also  of  62°  P.,  then  the  apparent  equivalent  of  the  metre  would  be  nearly 
39-382  inches. 

The  KILOGRAMME  is  the  weight  in  vacuo  at  o°  C.  of  the  platinum-iridium  weight  deposited  with  the 
Board  of  Trade.  * 

The  L.ITRB  contains  one  kilogramme  weight  of  distilled  water  at  its  maximum  density  (4°  C.),  the 
barometer  being  at  760  millimetres. 

*In  accordance  with  the  schedule  adopted  under  the  Weights  and  Measures  (metric  system)  Act,  1897. 
SMITHSONIAN  TABLES. 

5 


TABLE  2. 

EQUIVALENTS   OF   METRIC   AND    BRITISH    IMPERIAL   WEIGHTS 
AND    MEASURES. 

(2)    METRIC  TO   IMPERIAL 


LINEAR   MEASURE. 

MEASURE  OF  CAPACITY. 

I 

3 
4 
5 
6 

I 

9 

Millimetres 
to 
inches. 

Metres 
to 
feet. 

Metres 
to 
yards. 

Kilo- 
metres to 
miles. 

Litres 
to 
pints. 

Dekalitres 
to 
gallons. 

Hectolitres 
to 
bushels. 

Kilolitres 
to 
quarters. 

0.0393701 
0.0787402 
O.Il8lI03 
o.  1574804 
0.1968505 

0.2362206 

0.2755907 
0.3149609 
0.3543310 

I    3.28084 
3   6.56169 
4    9-84253 
5T3-I2337 
616.40421 

819.68506 
922.96590 
o  26.24674 

2  29.52759 

1.09361 

2.18723 
3.28084 
4.37446 
5.468o7 

6.56169 
7.65530 
8.74891 

9.84253 

0.62T37 

1.24274 
I.864I2 
2.48549 
3.10686 

3.72823 
4.34760 
4.97098 
5.59235 

I 

2 

3 

i   4 
5 
6 

9 

1.75980 
3.5I96I 
5.27941 
7.03921 
8.79901 

10.55882 
12.31862 
14.07842 
15.83822 

2.19975 

4.39951 
6.59926 
8.79902 
10.99877 

13.19852 
15.39828 

17.59803 
19.79778 

2.74969 
549938 
8.24908 
10.99877 
13.74846 

16.49815 
19.24785 
21.99754 

24.74723 

3-43712 
6.87423 

10.31135 
13.74846 
17.18558 

20.62269 
24.05981 
27.49692 
30.93404 

— 

SQUARE  MEASURE. 

WEIGHT  (AVOIRDUPOIS). 

Square 
centimetres 
to  square 
inches. 

Square 
metres  to 
square 
feet. 

Square 
metres  to 
square 
yards. 

Hectares 
to  acres. 

Milli- 
grammes 
to 
grains. 

Kilogrammes 
to  grains. 

Kilo- 
grammes 
to 
pounds. 

Quintals 
to 
hundred- 
weights. 

i 

2 

3 
4 
5 
6 

9 

0.15500 
0.31000 
0.46500 
O.6200O 
0.77500 

0.93000 
1.08500 
1.24000 
I-3950I 

10.76393 
21.52786 
32.29179 
43.05572 
5381965 

64.58358 
75.34751 
86.11144 

96.87537 

I-I9599 
2  39198 

3.58798 

4  78397 

5.97996 

7-17595 
8.37195 
9.56794 
10.76393 

2.47II 
4.9421 
7-4T32 
9.8842 

12-3553 
14.8264 
17.2974 
19.7685 
22.2395 

I 

2 

3 
4 
5 
6 

9 

0.01543 
0.03086 
0.04630 
0.06173 
0.07716 

0.09259 
0.10803 
0.12346 
0.13889 

15432.356 
30864.713 
46297.069 
61729.426 
77161.782 

92594.138 
108026.495 
123458.851 
138891.208 

2.20462 
4.40924 
6.61386 
8.81849 
II.023II 

13.22773 

15  43235 
17.63698 
19.84160 

1.96841 

3.93683 
5.90524 
7.87365 
9.84206 

11.81048 
13.77889 
15.74730 
17.71572 

CUBIC  MEASURE. 

APOTHE- 
CARIES' 
MEASURE. 

AVOIRDUPOIS 
(cant.) 

TROY  WEIGHT. 

APOTHE- 
CARIES' 
WEIGHT. 

Cubic 
decimetres 
to  cubic 
inches. 

Cubic 
metres  to 
cubic 
feet. 

Cubic 
metres  to 
cubic 
yards. 

Cub.  cen- 
timetres 
to  fluid 
drachms. 

Milliers  or 
tonnes  to 
tons. 

Grammes 
to  ounces 
Troy. 

Grammes 
to  penny- 
weights. 

Grammes 
to 
scruples. 

2 

3 

4 
5 
6 

8 
9 

61.02390 
122.04781 
183.07171 
244.09561 
305.11952 

366.  14342 
427.16732 
488.19122 
549.21513 

35.31476 
70.62952 
105.94427 
141.25903 
176.57379 
2H.88855 
247.20331 
282.51806 
317.83282 

1.30795 
2.61591 
3.92386 
5.23182 
6-53977 

7.84772 
9.15568 
10.46363 
11.77159 

0.28157 
0.56314 

o  84471 

I.I2627 
1.40784 

I.6894I 
1.97098 
2.25255 
2-53412 

I 

2 

3 
4 
5 
6 

9 

0.98421 
I.9684I 
2.95262 
3.93682 
4.92103 

5-90524 
6.88944 

7.87365 
8.85785 

0.03215 
0.06430 
0.09645 
0.12860 
0.16075 

0.19290 
0.22506 
0.25721 
0.28936 

0.64301 
1.28603 
1.92904 
2.57206 
3.21507 

3.85809 
4.50110 
5.14412 
578713 

0.77162 

!-54323 
2.31485 

3.08647 
3.85809 

4.62970 

5-4013! 
6.17294 

6.94455 

SMITHSONIAN  TABLES. 


TABLE  2. 

EQUIVALENTS   OF    BRITISH    IMPERIAL    AND    METRIC   WEIGHTS 
AND    MEASURES. 

(3)    IMPERIAL  TO    METRIC. 


LINEAR   MEASURE. 

MEASURE   OF  CAPACITY. 

f  25.400  milli- 

gill                            —  1.42  decilitres. 

i  inch    =  \        metres. 

i  foot  (12  in.)     .     .=       0.30480    metre. 

pint  (4.  gills)  .     .     .  =0.568  litre, 
quart  (2  pints)    .     .  =  1.136       litres. 

i  YARD  (3ft.)     .     .  =       °-9r4399 
i  pole  (5!  yd.)    .     .=       5-0292  metres. 

GALLON  (4  quarts)  =4.5459631  " 
peck  (2  galls.)    .     .  =  9.092 

i  chain  (22  yd.  or  )             20.1168       " 

bushel  (8  galls.)      .  =  3.637  dekalitres. 

100  links)         \ 
i  furlong  (220  yd.)  =   201.168         " 

i  quarter  (8  bushels)  =  2.909  hectolitres. 

i  mile  (1,760  yd.)    .  =  |     '"JjJ^jf16" 

AVOIRDUPOIS   WEIGHT. 

SQUARE   MEASURE. 

(64.8    milli- 

i  grain  .                     —  < 

(6.4516  sq.  cen- 

|     grammes. 

i  square  inch           .    =   \     timetres. 

dram  —      !-772  grammes. 

9.2903  sq.  deci- 

i  sq.ft.  (i44sq.  in.)    =  =           metres, 
f  0.836126  sq. 
i  SQ.  YARD  (9  sq.  ft.)  =    1      metres. 

ounce  (16  dr.)  .     .  =    28.350         " 
POUND  (16  oz.  or  I 
7,000  grains)      \=      o^5359243  kilogr. 
stone  (14  Ib.)   .     .=      6.350                 " 

f  2s?  201  SQ   me- 

quarter  (28  Ib.)     .=    12.70                   " 

i  perch  (30!  sq.  yd.)  =  |      'tres 

hundredweight  J           j  50.80                  " 

i  rood  (40  perches)    =     10.117  ares. 

(ii2lb.)         f      "  (   o!5o8o  quintal. 

i  ACRE  (4840  sq.  yd.)  =       0.40468  hectare. 

{i.  0160  tonnes  or 

i  sq.  mile  (640  acres)  =  ^259.00  hectares. 

1016    kilo- 

( 

grammes. 

TROY   WEIGHT. 

CUBIC   MEASURE. 

i  cub.  inch=    16.387  cub.  centimetres, 
i  cub.  foot  (1728  1        f  o.o283i7cuh.  me- 
cub.  in.)            f  —  \     tre,    or   28.317 
t    cub.  decimetres. 

i  Troy  OUNCE  (480  )  =               grammes. 
grains  avoir.)      ) 
i  pennyweight  (24)    __ 
grains)                 f 

UB'  YARD  (27  /  __  0.76453  cub.  metre. 

NOTE.  —  The  Troy  grain  is  of  the  same  weight  as 
the  Avoirdupois  grain. 

APOTHECARIES'   MEASURE. 

APOTHECARIES'   WEIGHT. 

i  gallon  (8  pints  or  )  _      4.5459631  litres. 
1  60  fluid  ounces)  J 
I  fluid  ounce,  f  3  )            (28.4123  cubic 
(8  drachms)       J       ~   f     centimetres. 

i  ounce  (8  drachms)   =  31.1035  grammes, 
i  drachm,  3  i  (  3  scru-  (  goo           <» 

•r\lpc\                                                (                    O" 

i   fluid  drachm,  f  3  )  f  3.5552  cubic 
(60  minims)          )  ~     \    centimetres. 

LUGS;             ^                  j 

i  minim,  n\  (0.91146  (  /  0.05925  cubic 

grams)                 ) 

grain  weight)       \  ~~   \    centimetres. 

NOTE.  —  The  Apothecaries'  ounce  is  of  the  same 

weight  as  the  Troy  ounce.      The   Apothecaries' 

NOTE.  —  The   Apothecaries'  gallon   is  of  the  same 

grain  is  also  of  the  same  weight  as  the  Avoirdupois 

capacity  as  the  Imperial  gallon. 

grain. 

NOTE.  —  The  YARD  is  the  length  at  62°  Fahr. ,  marked  on  a  bronze  bar  deposited  with  the  Board  of  Trade. 

The  POUND  is  the  weight  of  a  piece  of  platinum  weighed  in  vacuo  at  the  temperature  of  o°  C.,  and  which  is  also 
deposited  with  the  Board  of  Trade. 

The  GALLON  contains  10  Ib.  weight  of  distilled  water  at  the  temperature  of  62°  Fahr.,  the  barometer  being  at 
30  inches.  The  weight  of  a  cubic  inch  of  water  is  252.286  grains. 

SMITHSONIAN  TABLES. 


TABLE  2. 

EQUIVALENTS   OF    BRITISH    IMPERIAL    AND    METRIC    WEIGHTS 
AND    MEASURES. 

(4)    IMPERIAL  TO    METRIC. 


LINEAR   MEASURE. 

MEASURE  OF   CAPACITY. 

Inches 
to 
centimetres. 

Feet 
to 
metres. 

Yards 
to 
metres. 

Miles 
to  kilo- 
metres. 

Quarts 
to 
litres. 

Gallons 
to 
litres. 

Bushels 
to 
dekalitres. 

Quarters 
to 
hectolitres. 

I 

2 

3 
4 
5 
6 

I 

9 

2.539998 
5.079996 
7.619993 
10.159991 
12.699989 

15.239987 
17.779984 
20319981 
22.859979 

0.30480 
0.60960 
0.91440 
1.21920 
1.52400 

1.82880 
2.13360 
2.43840 
2-74320 

0.91440 
r.  82880 
2.74320 
3-65760 
4.57200 

5  48640 
6.40080 
7-31520 
8.22960 

1.60934 

3.21869; 
4.82803 

6-43737 
8.04671 

9.65606 
11.26540 
12.87474 
14.48408 

I 
2 

3 

4 
5 
6 

8 
9 

1.13649 
2.27298 

3-4C947 
4-54596 
5-68245 

6.81894 

7-95544 
9.09193 
10.22842 

4.54596 
9.09193 

13  63789 
18.18385 
22.72982 

27.27578 
31.82174 
36.36770 
40.91367 

3  63677 
7-27354 
10.91031 
14.54708 
18.18385 

21.82062 

25-45739 
29.09416 

32.73093 

2.90942 
5.8l883 
8.72825 
11.63767 
14.54708 

17.45650 
20.36591 

23.27533 
26.18475 

SQUARE  MEASURE. 

WEIGHT  (AVOIRDUPOIS). 

Square 
inches 
to  square 
centimetres. 

Square 
feet 
to  square 
decimetres. 

Square 
yards  to 
square 
metres. 

Acres  to 
hectares. 

Grains  to 

milligrammes. 

Ounces  to 
grammes. 

Pounds   \  Hundred- 
to  kilo-     weights  to 
grammes.  ;  quintals. 

2 

3 

4 
5 

1  6 

1 

9 

6.45159 
12.90318 

I9-35477 
25-80636 
32.25794 

38.70953 
45  16112 
51.61271 
58.06430 

9.29029 
18.58058 
27.87086 
37.I6II5 
46.45144 

55.74173 
65.03202 
74.32230 
83.61259 

0.83613 
1.67225 
2.50838 
3.34450 
4.18063 

5.01676 

5.85288 
6.68901 

7-525  r3 

0.40468 

o  80937 

1.21405 
1.61874 
2.02342 

2.428IT 
2.83279 

3.23748  : 
3.64216 

3 
4 
5 
6 

8 
9 

64.79892 
129.59784 
194  39676 
259-I9568 
323-99459 

388.79351 
453-59243 
518.39135 
583.19027 

28.34953 
56.69905 
85.04858 
113.39811 
141.74763 

170.09716 
198.44669 
226.79622 
255.14574 

0-45359  ]  0.50802 
0.90719  i  1.01605 
1.36078  j  1.52407 
i.  8  1  437  |  2.03209 
2.26796!  2.54012 

2.72156  i  3.04814 

3.I75I5    3-556i7 
3.628741  4.06419 
4.08233!  4.57221 

CUBIC   MEASURE. 

APOTHE- 
CARIES' 
MEASUKE. 

AVOIRDUPOIS 
(cont.). 

TROY  WEIGHT. 

APOTHE- 
CARIES' 

WEIGHT. 

Cubic 
inches 
to  cubic 
centimetres. 

Cubic  feet 
to 
cubic 
metres. 

Cubic 
yards 
to  cubic 
metres. 

Fluid 
drachms 
to  cubic 
centi- 
metres. 

Tons  to 
milliers  or 
tonnes. 

Ounces  to 
grammes. 

Penny- 
weights to 
grammes. 

Scruples 
to 
grammes. 

2 

3 
4 

5 
6 

8 
9 

16.38702 
32.77404 
49.16106 
65.54809 
81.93511 
9832213 

II4.709I5 
131.09617 
147.48319 

0.02832 
0.05663 
0.08495 
0.11327 
0.14158 

0.16990 
0.19822 
0.22653 
0.25485 

0.76455 
1.52911 
2.29366 
3.05»2I 
3.82276 

4.58732 
5.35187 
6.11642 

6  88098 

355153 
7.10307; 
10.65460 
14.20614 
17.75767 

21.30920! 
24.86074 
28.41227 
3I.9638IJ 

I 

2 

3 
4 
5 
6 

9 

1.01605 

2.03210 
304814 
4.06419 

5  08024 

6.09629 
7-11233 
8.12838 
9-  i  4443 

31.10348 
62.20696 

93-3I044 
124.41392 

155.5174' 
186.62089 
217.72417 
248.82785 
279.93133 

I-555I7 
3.110*5 
4.66552 
6.22O/O 
7.77587 

9-33I04 
10.88622 
12.44139 
I3-99657 

1.29598 
2.59196 

3.88794 

5-  i  S39i 
6.47989 

7-77587 
9.07185 
10.36783 
11.66381 

SMITHSONIAN  TABLES. 


TABLE  3. 
TABLES  FOR  CONVERTING  U.  S.  WEIGHTS  AND  MEASURES.* 

(I)   CUSTOMARY  TO   METRIC. 


LINEAR. 

CAPACITY. 

Inches 
to 
millimetres. 

Feet  to 
metres. 

Yards  to 
metres. 

Miles 
to 
kilometres. 

Fluid 
drams  to 
millimetres 
or  cubic 

Fluid 
ounces 
to 

Quarts  to 

litres. 

Gallons  to 
litres. 

centimetres. 

millilitres. 

I 

2 

25.4001 
50.8001 

0.304801 
0.609601 

0.914402 
1.828804* 

1.60935 
3.21869 

2 

3-70 

7-39 

jw 

0.94636 
1.89272 

3.78543 
7.57087 

3 

76.2002 

0.914402 

2.743205 

4.82804 

3 

11.09 

88.72 

2.83908 

H.35630 

4 

IOI.6OO2 

I.2I9202 

3.657607 

6-43739 

4 

14.79 

118.29 

3.78543 

15.14174 

5 

127.0003 

1.524003 

4.572009 

8.04674 

5 

18.48 

147.87 

W3179 

18.92717 

6 

152.4003 

1.828804 

5.486411 

9.65608 

6 

22.18 

177.44 

5-678I5 

22.71261 

7 

177.3004 

2.133604 

6.400813 

11.26543 

7 

25.88 

207.02 

6.62451 

26.49804 

8 
9 

203.2004 
228.6005 

2.438405 
2.743205 

8.229616 

12.87478 
14.48412 

8 
9 

29-57 
33-27 

236.59 
266.16 

7.57087 
8.51723 

30.28348 
34.06891 

SQUARE. 

WEIGHT. 

Square 
inches  to 
square  cen- 
timetres. 

Square  feet 
to  square 
decimetres. 

Square 
yards  to 
square 
metres. 

Acres  to 
hectares. 

Grains  to 
milli- 
grammes. 

Avoirdu- 
pois ounces 
to 
grammes. 

Avoirdu- 
pois pounds 
to  kilo- 
grammes. 

Troy 

ounces  to 
grammes. 

I 

6.452 

9.290 

0.836 

0.4047 

I 

64-7989 

28.3495 

0-45359 

31.10348 

2 

12.903 

18.581 

1.672 

0.8094 

2 

129.5978 

56.6991 

0.90719 

62.20696 

3 

19-355 

27.871 

2.508 

1.2141 

-^ 

194.3968 

85.0486 

1.36078 

93-3  T  044 

4 

5 

25.807 

32.258 

37.161 
46.452 

3-344 
4.181 

1.6187 
2.0234 

4 

5 

259.1957 

113.3981 
141.7476 

1.81437 
2.26796 

124.41392 

i55-5I74Q 

6 

38.710 

55-742 

5.017 

2.4281 

6 

388.7935 

170.0972 

2.72156 

186.62088 

8 

45.161 
5I-6I3 

65.032 
74.323 

5.853 
6.689 

2.8328 
3-2375 

8 

453-5924 

5I8-39I4 

198.4467 
226.7962 

3-I75I5 
3.62874 

217.72437 
248.82785 

9 

58.065 

83-613 

7-525 

3.6422 

9 

583-1903 

255-I457 

4.08233 

279-93I33 

CUBIC. 

Cubic 
inches  to 
cubic  cefi- 
timetres. 

Cubic  feet 
to  cubic 
metres. 

Cubic 
yards  to 
cubic 
metres. 

Bushels  to 
hectolitres. 

i  Gunter's  chain  =      20.1168         metres, 
i  sq.  statute  mile  =    259.000        hectares. 

i  fathom               =        1.829           metres. 

I 

2 

16.387 
32-774 

0.02832 
0.05663 

0.765 
1.529 

0.35239 
0.70479 

i  nautical  mile     =  1853.25              metres. 

3 

49.161 

0.08495 

2.294 

1.05718 

i  foot                    =        0.304801        metre. 

4 
5 
6 

81^36 
98.323 

0.11327 
0.14158 

0.16990 

3.058 
3.823 

4.587 

1.40957 
1.76196 

2.11436 

i  avoir,  pound     =    453.5924277  gramme. 
1  5432.  35639  grains  =        i  .000  kilogramme. 

7 

114.710 

0.19822 

5-352 

2-46675 

8 

i  a1  -°97 

0.22654 

6.II6 

2.81914 

9 

147.484 

0.25485 

6.881 

3-I7I54 

The  only  authorized  material  standard  of  customary  length  is  the  Troughton  scale  belonging  to  the  United  States 
Office  of  Standard  Weights  and  Measures,  whose  length  at  59°.62  Fahr.  conforms  to  the  British  standard.  The  yard 
in  use  in  the  United  States  is  therefore  equal  to  the  British  yard. 

The  only  authorized  material  standard  of  customary  weight  is  the  Troy  pound  of  the  Mint.  It  is  of  brass  of  un- 
known density,  and  therefore  not  suitable  for  a  standard  of  mass.  It  was  derived  from  the  British  standard  Troy 
pound  of  1758  by  direct  comparison.  The  British  Avoirdupois  pound  was  also  derived  from  the  latter,  and  contains 
7,000  grains  Troy. 

The  grain  Troy  is  therefore  the  same  as  the  grain  Avoirdupois,  and  the  pound  Avoirdupois  in  use  in  the  United 
States  is  equal  to  the  British  pound  Avoirdupois. 

The  British  gallon  m    4.54346  litres. 

The  British  bushel  =  36.3477    litres. 

The  length  of  the  nautical  mile  given  above  and  adopted  by  the  U.  S.  Coast  and  Geodetic  Survey  many  years 
ago,  is  defined  as  that  of  a  minute  of  arc  of  a  great  circle  of  a  sphere  whose  surface  equals  that  of  the  earth  (Clarke's 
Spheroid  of  1866). 

*  Quoted  from  sheets  issued  by  the  United  States  Office  of  Standard  Weights  and  Measures. 
SMITHSONIAN  TABLES. 

9 


TABLE  3. 

TABLES  FOR  CONVERTING  U.  S.  WEIGHTS  AND  MEASURES. 

(2)    METRIC  TO  CUSTOMARY. 


LINEAR. 

CAPACITY. 

Millilitres 

or  cubic 

Centi- 

Deca- 

Hecto- 

Metres to 

Metres  to 

Metres  to 

Kilometres 

centi- 

litres to 

litres 

litres 

inches. 

feet. 

yards. 

to  miles. 

metres 

fluid 

to 

to 

to  fluid 

ounces. 

gallons. 

bushels. 

drams. 

I 

39-3700 

3.28083 

1.093611 

0.62137 

I 

0.27 

0.338 

1.0567 

2.6417 

2.8377 

2 

78.7400 

6.56167 

2.187222 

1.24274 

2 

0-54 

0.676 

2.1134 

5.2834 

5.6755 

3 

IlS.IIOO 

9.84250 

3.280833 

1.86411 

3 

0.8  1 

I.OI4 

3.1700 

7-9251 

8.^132 

4 

157.4800 

I3-I2333 

4-374444 

2.48548 

4 

1.  08 

J-353 

4.2267 

10.5668 

11.8510 

5 

196.8500 

16.40417 

5.468056 

3.10685 

5 

1-35 

1.691 

5-2834 

13.2085 

14.1887 

6 

236.2200 

19.68500 

6.561667 

372822 

6 

1.62 

2.029 

6.3401 

15.8502 

17.0265 

7 

275.5900 

22.96583 

7.655278 

4-34959 

7 

1.89 

2.367 

7.3968 

I8.4QI9 

19.8642 

8 

314.9600 

26.24667 

8.748889 

4.97096 

8 

2.16 

2.705 

8-4535 

21.1336 

22.7019 

9 

354-3300 

29.52750 

9.842500 

9 

2-43 

3-043 

9.5101 

23-7753 

25.5397 

SQUARE. 

WEIGHT. 

Square 

Square 

Square 

Milli- 

Kilo- 

Hecto- 

Kilo- 

centimetres 

metres  to 

metres  to 

Hectares   | 

grammes 

grammes 

grammes 

grammes 

to  square 

square 

square 

to  acres. 

to 

to 

to  r 

unces 

o  pounds 

inches. 

feet. 

yards. 

grains. 

grains. 

avoirdupois. 

avoirdupois. 

I 

0.1550 

10.764 

1.196 

2.471 

I 

0.01543 

15432.36 

•S274 

2.20462 

2 

0.3100 

21.528 

2.392 

4.942 

2 

0.03086 

30864.71 

7.0548 

4.40924 

3 

0.4650 

32.292 

3.588 

7-4I3 

3 

0.04630 

46297.07 

10.5822 

6.61387 

4 

O.62OO 

43-055 

4.784 

9.884 

4 

0.06173 

61729.43 

14 

.1096 

8.81849 

5 

0.7750 

53-8I9 

5.980 

12-355 

5 

0.07716 

77161.78 

17.6370 

[I.O23II 

6 

0.9300 

64-583 

7.176 

14.826 

6 

0.09259 

92594.14 

21 

.1644 

I3-22773 

7 

1.0850 

75-347 

8-372 

17.297 

7 

0.10803 

108026.49 

24.6918 

15-43236 

8 

1.2400 

86.1  1  1 

9.568 

19.768 

!  8 

0.12346 

123458.85 

28.2192 

17.63698 

9 

1-3950 

96-875 

10.764 

22.239 

9 

0.13889 

138891.21 

31 

.7466 

19.84160 

CUBIC. 

WEIGHT. 

Cubic 
centimetres 
to  cubic 

Cubic 
decimetres 
to  cubic 

Cubic 
metres  to 
cubic 

Cubic 
metres  to 
cubic 

Quintals  to 
pounds  av. 

Milliers  or 
onnes  to  pounds 

Kilogrammes 
to  ounces 

inches. 

inches. 

feet. 

yards. 

I 

0.06  1  o 

61.023 

35-3I4 

1.308 

I                220.46 

2204.6 

32.1507 

2 

0.1220 

122.047 

70.629 

2.616 

2                440.92 

4409.2 

64.3015 

3 
4 

0.1831 
0.2441 

183.070 
244.094 

105-943 
141.258 

3-924 
5-232 

3            661.39 
4            881.85 

6613.9 
8818.5 

96.4522 
128.6030 

5 

0.3051 

305.H7 

176.572 

6.540 

5          1102.31 

11023.1 

160.7537 

6 

0.3661 

366.140 

211.887 

7.848 

6          1322.77 

13227.7 

192.9044 

£ 

0.4272 
0.4882 

427.164 
488.187 

247.201 
282.^16 

9.156 
10.464 

7           I543-24 
8           1763.70 

15432.4 
17637.0 

225-0552 
257.2059 

9 

0.5492 

549.210 

3I7-8;30 

11.771 

9          1984.16 

19841.6 

2< 

^-3567 

By  the  concurrent  action  of  the  principal  governments  of  the  world  an  International  Bureau  of  Weights  and 
Measures  has  been  established  near  Paris.  Under  the  direction  of  the  International  Committee,  two  ingots  were  cast 
of  pure  platinum-indium  in  the  proportion  of  9  parts  of  the  former  to  i  of  the  latter  metal.  From  one  of  these  a  cer- 
tain number  of  kilogrammes  were  prepared,  from  the  other  a  definite  number  of  metre  bars.  These  standards  of 
weight  and  length  were  intercompared,  without  preference,  and  certain  ones  were  selected  as  International  prototype 
standards.  The  others  were  distributed  by  lot,  in  September,  1889,  to  the  different  governments,  and  are  called 
National  prototype  standards.  Those  apportioned  to  the  United  States  were  received  in  1890,  and  are  kept  in  the 
Office  of  Standard  Weights  and  Measures  in  Washington,  D.  C. 

The  metric  svstem  was  legalized  in  the  United  States  in  1866. 

The  International  Standard  Metre  is  derived  from  the  Metre  des  Archives,  and  its  length  is  defined  by  the  dis- 
tance between  two  lines  at  o°  Centigrade,  on  a  platinum-iridium  bar  deposited  at  the  International  Bureau  of  Weights 
and  Measures. 

The  International  Standard  Kilogramme  is  a  mass  of  platinum-iridium  deposited  at  the  same  place,  and  its 
weight  in  yacuo  is  the  same  as  that  of  the  Kilogramme  des  Archives. 

The  litre  is  equal  to  a  cubic  decimetre,  and  it  is  measured  by  the  quantity  of  distilled  water  which,  at  its  maximum 
density,  will  counterpoise  the  standard  kilogramme  in  a  vacuum,  the  volume  of  such  a  quantity  of  water  being,  as 
nearly  as  has  been  ascertained,  equal  to  a  cubic  decimetre. 

SMITHSONIAN  TABLES. 


CONVERSION    FACTORS. 


TABLES  4,  5. 


-J 
II 

8 

o 

* 

i 

VO   ON  -    O  CO 

PI    PI    ON  Tf  Tf 
V0to«    w    O 

1 

Q 

Centimet 

6 

"b"©  o  o 
XXXX 

^^•80  8H 

ON  to  ~^t"CO    O 
O    to  Tf  Tf  rf 
VO  00   •-   O   to 

«    «    ON  (ON 

i 

H-    O   O  OO        VO 

—    tOvO   ON^^  to 
O  vO  to  r^*^  ON 
oq  oq  toq        to 

rj-  ^  -    M         |M 

S 

l"" 

6 

^  'o  o  o      o 
XXXX     X 

JM   O   O  iH   Q 
^o  o  o       r^ 
ro  oj  vo  w        ON 

i 

5 

! 

OC?M       S^cc" 
\O  ON  •^       oo  ON 

N  co3  r^°  8  ^ 

tv.  (v.  ^-           OJN  tO 

f  O  ro  O       1  «^  1  N 

! 

i 

J 

i 

"22        2^2 
XX     HXX 

PI   O   O         to  N 

i 

to\o  o  ri  toco 

toto     IN-ININ 

9 

O  O        O  O  O 

3 
* 

i 

*• 

XXHXXX 

vo  M        to  t^  ON 

r>q      ^r^q 

1-1    PI          fO  PI    i-« 

H 

4 

i 

«          ON  t-x  O^vO 
r-»       i-  Qoo  O 
00  O  tovO  vO  M 

tO^1*    ON  1-1    fO  fO 

ON     vq  N  «  r>. 

Nautical  n 

6 

X     XXXX 

§»§!?§; 

oo        to  ^  r^>  ON 
vq       ONVO  to  to 

OO               TJ-   M     t-4     10 

i 

ON  r^vO  to  o 

oo  oo  vOoo  to 

N    -^-  fO  «    fO 

^N     H^     Tt"   ^^OO     tO 

9*Q  to  r^  ON  ON 

/  q  t>  M  w  t> 

Statute  m 

6 
K 

2T2kT2 

XXXX 

^1  r*^.  w  ^i*oO  O 

UOOQ    Q\  C^l    t^N, 

s 

II 
1 

0 

£ 

i 

O  tow   O  1-1 

^}-    H,     J^   w      Tf 

tO  10  M    ON  M 

RpT32  p?° 

to  ONOO  vd  tr> 

n 

i 

1 

"3 

Vo-b^o 

5 

g 

g 

* 

xxxxx 

rf  «    M    M    to 

>-<   O   ON  to  to 
~  vq  CO   M   ON 

| 

1 

^ 

ON  i-^  tovQ         to 

•*f  ON  ONOO        r^ 
O  to  PI  O       |vO 

Square  centi 

6 

1*22        ?2 
xxx    Hx 

to  ro  t*i   TJ-       o 

i 

5 

^ 

JZ 

J 

Q    to  W             i-*     O 

row  co_o  2.  ""> 

oSfON       l~lr^ 

£ 

'b'b'b     'o'o 

1 

I 

I 

1 

6 

XXX     XX 

ON  O    O  '"'    QOO 

^*  O  O        O  ON 
T}-VO  O        O  to 

i-.    ON  -^f          to  IO 
O    M    ^t-          "TOO 

3 

^ 

| 

«J 

i 

00    M           I-^OO    t^ 
VO    rj-         fOv£>    M 

tOTt-Q     NH     1-     t-^ 

-fr  10*^  Tf  r<->  PO 
-<t  ON      00  0  r;. 

! 

0 

§ 

3 
O" 
CO 

i 

T  7    T 

x>          o  o  o 

x    Hxxx 

CO   8         rf  ror^ 
N   ON      \o  «  to 

H 

i 

to        i^  tovO  to 
JJ         "^  ON  P«  oo 
O        i^  ^o  r^*  ^T 

ONO  -3-co  t^oo 
rj-       OCQ  O  r~* 

vd     in;i4i4|6 

1 

6 

£ 

*b      o  o  'o  o 
X      XXXX 

0  l~l  «  tox5  r^ 
t>*»        **  vO   to  O 

O\          (-!>-<    ONVO 

ro       «   t^-  -  vd 

. 

1 

to  PI    O   O   O 
f>,rOrv,  OvO 

-_  CO   ^-vo'vo"  i- 
O   O  to  ONOO   ON 

to  VO  tO  to  P4 

i 

r-    oo    S    S    S 

'o  'o  'o  'o  'o 

CO 

* 

Hxxxxx 

fO  O   ON  O   "<*• 
00   r^  O   I-  vO 
PI  OO   ONVO  to 
M  10  rj-oo  ON 

SMITHSONIAN  TABLES. 


II 


TABLES  6,  7. 


CONVERSION   FACTORS, 


a 

u 

f 

00    OvO   N 

Dimensions  = 

c  centimetre. 

HJ 

vo  co  ^r  cj 
IOVOTJ-  « 

!r°° 

JS 

a 

0 

XXXX 

to  loco  "-1  H 

OO    to  >-i  OO 

vo  rf  roro 
«VOOOVO 

rj-  r^  M  I-H 

10  I^  rf        00 

Tf1  O   ^J"        ON 

I 
u 

3 

u 

5 

o'vO    roO  co"" 

6 
£ 

XXXX 

OO   O    O  '"'  vO 

tovo   O         co 
ro  LOOO         N 

«    *  "        ^ 

ibic  foot. 

i 

O  vo         to  10 

ON  ro        rt-  ON 

'bo      'o  o 

CJ 

6 

XX      XX 

J^Q       Q    1-4        ^     J 

ON  o         O   ^" 
rf  i^       r>»  «-o 

i 

OO         VO    N    O 
CO        roQ>  ON 
LO      vo   O   to 

vo  o  °2  "-1  ^ 
ro       vO   co  >-i 

0 

OS      ir^l^vd 

°o       boo 

£ 

. 

X     XXX 

* 

oo  ^  o  ^  to 

to         CO  N    HH 

M  00    tON 

I 

i 

TJ-  o  "TO1 

,*.    ro  N   Tf  O 
O  VO   fOONCO 
cioo  toro 

id  ^1^^ 

7  f  T  7 

3 

U 

d 

55 

XXXX 

Hvo   f^-^O 
Tf-  co  O   r-^ 

•sfii 

u 
i 

i 

i 

i 

\O  N   rt-  r-, 
•«*•  O   -   O 
0  to^«   r^ 

Tf  M    VOVO 

2j«i  o*  d 

0   0 

0 

XX 

CO    M    C)    WH 

CO  rooo   "^ 

oo  vo  t^.  "^ 

c4   I-H   co  •<}• 

ON  to  t^        N 

ish  gallon. 

5 

i^.  to  ON       co 

O|COi«          |M 

ToTo      7o 

6 

XXHX 

CO    O   rf        ro 
r--.  ^  to       ON 
c-4   O  cj         ON 
CM  vp   ro       M 
vd  coco         ci 

States  gallon. 

i 

coco         ONCO 
ON  ro        tooo 

CO  O          O    rf 

d  i  co      d  i  * 

C5                          rl 

b             b 

"S 
P 

6 

4H-^ 

CO    CM           O    1^- 
•^-  CO        M  vO 

.5 

u 

s 

5     2S"& 

to        VO    C1    "^" 

r^Q  co  ro  to 

CO       VO    Tt-OO 
•    M         ro  TJ-  f^ 
co       cJ   ci  w 

«Q       cbcbo 

.0 

3 

U 

6 

X      XXX 

CO           O    ^f  M 

M         i—   r^.  o 

M         ri   ci  vd 
* 

WI 

Tf*  O  vO   ON 

1 

.a 

j 

vO   ci   O   "^1" 

mi 

3 

O 

6 

XXXX 

^   ^  i-^  ON  r^ 
O  CO  vO   •* 

co"  ro  b   ro 
r^  covo  to 

vo~   w   ro 

SMITHSONIAN  TABLES. 


12 


CONVERSION  FACTORS. 


TABLES  8.  9. 


s 

JJ|\ 

s 

S 

q  qvo  oq 

o 

0  ionic* 

1 

I 

E 

rS 

'^oVo 

0 

M       M       _,       »_ 

. 

xxxx 

* 

LOVQ     CO  O^ 

O  c/0    OOO 
vO    >—    10  <7\ 

o  q  u°"3- 

1 

VOCOCO         c^ 
S^CO         ^ 

r^»  t^«  ^o       H-I 

c 
1 

'b  'b  "o       o 

O 

_              _              _ 

XXX      X 

6 

_J 

£ 

000          C) 

II!  ? 

! 

°^-^       S  co 

S  20^^ 

LT)  O              >-O  Tf 

coco     l^ico 

rs 

3 

CO     05             T       I 

O    O          O    O 

0 

XX      XX 

TJ-  o         o    O 

ci  q       f  PI 

W) 

00           0^  CJ^g- 

c 

o 

,3 

f°^g- 

£_ 

d      i  ^106  iv6 

W   0 

o  § 

III 

6 

XXX 

,5 

O         O  vO   »—  ' 

CJ          0    rf  O 

e 

1 

ci   CJ   -3-vO 
OO    tj~>  ^OOO 

1 

|«|-*66l»>. 

|I 

7  T  T  7 

0000 

•1^ 

XXXX 

;c 

6 

H     t^   CV^OLT) 

PQ 

* 

u->  ci  >-o  o 

00    "*•  J^  ci 

CI  VO     I^*  Tt" 

O  T(-  COOO 

oo  "^vo  o^ 

.SP 


•5« 
5/.P 


I1 
i! 

li 

il 


II 

E 


II 


II 

M 

'a 

i 

vO   covO 
nvo  r^'® 

VO     Tfl^ 

s 

u 

vOCOw 

.£ 

E 

B 

QJ 

S 

2 

C 

222 

c 

£ 

w 

XXX 

.§ 

o 

ci  o  "^iH 

e 

* 

°}-vo"  O 

CJ 

III 

1 

O^r^       ^~ 
«-ovC  O   O 

Tj-OO   ^     CJ 

« 

M 

00  O         ci 

"5 

're 

T 

O 

^  2     2 

I 

1 

XX     X 

_j 

O  vO        vO 

c  oq      vq 

i 

CJ                Tj-    V 

ci       |rJ|^- 

"S, 

£> 

-a 

s 

§ 

(N               1        1 

PH 

2     22 

| 

J 

X      XX 

?    q1^- 

^           N    CO 

« 

* 

CO    >->    CO 

1 

f  t  f 

222 

0 

6 

XXX 

bo 

rH  ^.  js^  ^) 

rj-  10  O 

TfOO   co 

O>  ^f  co 

vb  -J  pi 

SMITHSONIAN  TABLES. 


TABLES  1O,  11. 


CONVERSION   FACTORS. 


Dimension  =r  1. 

u 

» 

O  •<}• 

j  3" 

!_, 

"8 

o'o 

1    c 

6 

XX 

~  p-J 

, 

i 

H 

o 

i 

X 
»o      ro 

A 

00  O 

r^co 

Radian. 

J 

M    t^ 

u 

6 

XX 

10  fO 

Jo 

SMITHSONIAN  TABLES. 


H 

II 

* 

loo^co  O 

I 

§ 

ON  ON  LO  i^ 

^  Tf  ro  J 

I 
0 

1 

"o'o'b  o 

c 

xxxx 

3 

O 

^8  o  8H 

o  o  o  o 

i>.O   *-o        ^~ 

—  m  -      oo 

0 

Jj 

r^ooooo  - 

10  10  t^.          PI 

•5 

roro-       IN 

!                 1-1 

1 

boo       o 

C 

s 

6 

XXX      X 

£ 

ty  i 

1 

-1-  —          CN  f^~ 
O   PI        cx^  O 

||°  gS 

3 
O 

-   -       IPI  l^r 

| 

o  o       o  o 

• 

6 

XX      XX 

^ 

^ 

u-i  O  '"*   r^oo 

2 

^   ?? 

bo 
o 

CO           •  ..o'  ^ 

i°£3r? 

ON       O  CO    O 

5 

'-        1^1-^1^ 

c 
i 

X     XXX 

fc 

°.H  ^^^. 

*. 

1 

oo  r-^.  M  r^ 

Q 

1 

"7*? 
boo 

.1 

C/3 

6 
fc 

XXX 

O  t^vO  VO 

TABLES  12,  13. 


CONVERSION   FACTORS. 


js  per  second. 

I 

Tf    M      QN  Tf 

H%o 

VO     Tf    Tf    M 
M'     M     M      O 

O   0   O 

Centimetr 

1 

XXX 

Tf  o  i>vq 
Tf  coc-i  M 

f 

&VO    °f        ^ 

Tf    -,    00                M 

00    0    M  Q  00 

£ 

3 

c 

TJ 

| 

Tf  ci  ci        r^. 

000         0 

1 

0 

XXX      X 

Tf    O     t^              O 

M  OO  VO           Q 

OO    M  VO           O 
VO  OO  vO         O 

'   0 

ifl 

I 

i 

&<£     £,£ 

d  d      IN  IN 

2  2 

s 

6 

O   ON        O   Q 

MM             VO     CO 

» 

ro       00    f.OO 
ro      vo  oo   ON 

M! 

^        ONr^^o 

1 

0         IMJNIN 

III 

I 

fc 

d 
X 

XXX 

t       Tf  r^  T$- 
Tf    O  OO 

Tf              M      Tf    ^ 

tO   M   ro 

1 

3 

ro  v/vo 
OO   l^.  to  fO 

III! 

J 

9 

& 

xxxx 

HcS^o< 

OO   rOOO  VO 

oq  N  r^.  N 
\d  vd  <o  N 

r^»oo  o  ON 

t^   N   00     Tf 

C? 

00    Q   M  00 

c 

1-5 

M    O    ^-  ^' 

§ 

If^M    O|N 

i. 

?nr    ^ 

9 

o  o      o 

0 

XX     X 

(5 

fl 

f~>  N    ^  VO 

Tf    Tf  00  VO 

"3 

i 

IIS        ? 

e 

|M    0    CO          M 

1 

o      'b      o 

J 
1 

PH 

d 

* 

XXX 

Tf  OO  vO         O 

t^  ON       O^  O 

bJD 

vo  oo      vo  oo 

T3 

O 

ro  >_<  o   ro  M 

0 

H-l 

Tf  M  ^    M    O 

Tf  M         Tf  n 

i 

iTfIN         1^1  ^ 

& 

T  ™     "7 

c 

o  o       o  o 

i 
•3 

i 

XX      XX 

oo  r^r"'  oo  to 

CJ 

t^xVO         N   *^ 

;r§  f? 

OJ 

3 

3 

ON        M^O    N^ 

OO         M  oo    ON 

nO^o^ 
N        r~»  M  ON 

a 

IN           M'|M    O 

& 

IM                         JH 

1                 1 

c 

0         O    0 

'•g 

X     XX 

1 

% 

VO         O  to  Tf 

<y 

vO         O   **   ON 

W 

vo         O  ""^  to 

M             VO     M      0\ 

M   ro  M  ro 

, 

3 

to  o  r^  N 

M   ro  ON  M 
Q  OO  vO  ONOO 
r~-  >-o  j^  vo 
t^»  to  ON  r^. 

o 

M  ro  d  N 

I 

G 

O  °O       ^b 

1 

XX     X 

1 
1 

* 

H  O  O  Tfoo 

O     O     Tf    VO 

Q  Q  ON  ON 

O  vO  to  r^ 

vd  roONto 

SMITHSONIAN  TABLES. 


TABLES  14,  15. 


CONVERSION    FACTORS. 


H 

M 

H«8 

H 
v^ 

_j 

i 

o 

NJ 

^     Tf   ONO° 

3 

% 

i| 

r^.  Tf  d  ^o 

i 

II 

ii 

• 
§ 

"i 

li 

"22    "2 

I 
s 

ji 

u 

1 

XX     X 

ON  "TOO  O  H 
Tf  <-o  O   O 
\o  N   »-o  O 

Q 

??!§ 

I. 

3 

oo  o  """O  Q 

, 

I 

fl 

0 

XXXHX 

"S 

| 

s 

Tf   >-OO              O 

€ 

•s 

Tf    M      W                W 

1 

Cvcg^       vovo 

•s 

1 

-d 

i 

11°  1  1 

1 

1 

<*L 

t^ro        Tf|« 

PI 

1 

c.ti 

P 

X 

0 

'o'o    •'o  o 
XX     XX 

w 
* 

1 

ft 

ro  O  ^  <•>  ON 

B 

M 

§ 

to  o         (^O  ro 
*-O  O         MD  MD 

q  q       q  q 

1 
§ 

s 

i 

3 

c 

3 

w           04  00  00 

ro       ON  ro  ro 
\O         ^T  "^  "^ 

Tf              M   OO  OO 

O 

S 

1 

CO      iTfOI^O 

1 

H 

11 
" 

M     TQ     ^ 

id 
H 

0 

XXX 

i 

1 

ft 

f)^  r^.  O   O 

H 

F1 

ro      oo   fO  fO 

fO        M   ro  ro 

ON          Tf  M    C) 

ON  >—  <  \O  *O 
ro  Tf  to  »-O 

W> 

vO   to  ON  ON 

o 

•*J 

4 

^00    SS 

£"0 

|Tfi>6ifO'c6 

g  - 

TOO      ^      00 
T  i  f 

K  II 

0   0   0   0 

jpf 

XXXX 

*«  c 

o 

to 

H  ON  no  O 

6  >-  oo  oo 

M  O_ 

ON  o  "^  1O 

Tf  C»"    Tf    Tf 

letre  Gramme 
ond  Units. 

i 

TfvO   ON  O  O 

22  2*2 

.5  S 

XXXX 

1 

2 

0    Tf  0    8H 

TfvO   O   Q 

— 

r  j  ON  q  q 

! 

OO^O    O         O 
ON  f)  O         Q 
vO   ro^O         O 
^•vO    C^Q    O 

I 

H 

Slid  .2. 

poo      o 

I1 

C5 

XXX     X 

So  N       Q 
Tf  O         Q 

M   ON  O        O 

Tf    NVO                I-l 

1 

MO   O 
)        O   O 
Tf    Tf 

sf 

M    N 

*b  o     ^  o 

-I 

0 
to 

XXHXX 

O  CO        ^O  ^O 

t 

ro       o  ^O  vO 

11 

N       loi   r^Tf 

i 

X      XXX 

Tf             VO  -      ^ 
Tf              0      Tf    Tf 

~         oi   roro 

1 

S 

t^>  M    P4    M 

rod   0   0 

\O   ON  ro  ro 

Q     _,     Tf   10  10 

oo    M.    ro  ro 
|  fOi  Tf  w  |\O 

o  o  o  o 

I 

6 

to 

XXXX 

H  Tf  r-~  N  N 

Tf  00   fO  ro 

Tf  N    Jv.  t^ 

ON  Tf  ro  <~O 

vd  «  ci  <4 

SMITHSONIAN  TABLES. 


16 


CONVERSION    FACTORS. 


TABLES  16,  17, 


S 

vO  vooo 

_J 

S 

I 

3-?^° 
r>»  t^*oo 

i'l 

.2 

rH     0 

£ 

§  8 

b'owo 

h 

te*  o> 

Q 

1 

XXX 

O  O  Q  H 

III 

7 

0000           N 

roro       ON 

C 

J? 

LO  *-O         *-O 

oq  oq       « 

•^3    cy 
C  C/3 

bfo      t 

(2 

1 

XX     X 
o  o  H  •^- 

O   O         lo 

§ 

fOCO       OO 

fOfO         N_ 

o      oo  oo 

Q         VO    1O 

| 

5 

0/^0*0 

0°  ^  ON 

£ 

'       vf  * 

"t       00   -f 

SS 

"o     "b'b 

S   0 

11 

. 

X      XX 

B 

55 

8          io  O* 

" 

O           W    »O 

'S 

i 

O    M    "<^ 
8    •-    N 

M 

Q  u 

I* 

O 

d 

XX 

• 
u 

ft 

H  O  jo  ^. 
O  M  *o 

o  oo  r^ 

n 


B  g 

si 

II 

a 


«] 

«i 
I  if 

Sl 


3* 


per  mi 
per  ho 


per 
er 


i 


i 


r^vo  vo 
•*T  ON  *-H 

*•<   O 


o  o  o  o  o 
XXXXX 

O  r^  -i  00  ro1 

IM^f 

•4-  t^.  COC4    rf 


>-   O  O   1-1  **• 

O  "^  t^  ^^"i  ^o 

O^  \O   rr  —  Tf 

rj-vo  oo  oo  o  •* 

oc  o  i-  r^  ro 

ON  w  oo  r-x  fO 

«   0  «   «  0 


0         O   O 

X      XX 


LO  C  OO   O 
VO  O   •-O  O 

ON  *"  vd  vd 


O  00  00         ON  N 

10  O  •  i-  Tt  O 

rj-  ro      oc    f) 


VO  00 

O  N  ^ 
M  Tf  O 
O'lN  O 


I        11 
X         XX 

tooo  *  fl 


^\ 
O  C 
vO  v 


h-.  O  **  O  •* 
rooo  oo  rooo 
ro  —  vO  LO  ON 


xxxx 


-    -  CO 

I-H     LO  M 


w         O   w   O 

^0         N    O 

< 


o      o  o  b 
X      XXX 


OO  fO  N 

^  M    —    TJ- 

r^  ^   ^O 


CN  CN  O   CN  CD 

TfO    LO  ON  10 

OO  vO  ro  w  vO 
•—  •   ro  ro  LO  ON 


XXXXX 
i-^oo  *•««>) 


VO  OO    N    O 

>->  vd  vd  i— 


SMITHSONIAN  TABLES. 


TABLES  18,  19. 


CONVERSION    FACTORS. 


$ 

* 

ON  r-^  O  ONr>- 
N  t^oo  •*  ON 

O  oo  >-i  00  vO  _. 
Q  «  00   •-"  roO 
N   •*  ON  M   <^- 
O  N  r^  n  ^f 

l«|fOO|C4|TJ- 

C    W 

.2  a 

si 
1 

1 

7  T     T  T 

00         00 

XX     XX 

O  ro  ON  r^oo  " 
w  ro«  vo  r^ 
t^  LO  rovO  t>» 

Tf   TfOO  VO     t^ 

O  r^.  N  vD  r^ 

M  M  \o'  «  r^5 

p 

i 

£  S 

! 

i-   O   N   w         ro 
moo  oo  LO      O 
ro  w    Tf  M         co 
vo  co  Ti-oo  O  ^ 
r^  ON  >-o  r^       LO 
to  r^  ro  r^       >-o 
M  O  •<*•  «        ro 

Radiar 
per  min.,  p 

I 

'o     "b  o     'o 
X     XX     X 

M    Q\  i_o  O  *-J    O 

ON  i-   ON  O         O 
ON  ro  *—  <   O         Q 
VO  OO  vO   Q         O 

fOvd   N  VO         co 

n.,  per  sec. 
.,  per  min. 

i 

OOO   «         ON« 
OO    N    fO         Tf  to 
I-H    O    fO       00    HH 
OO  O  VO  O  "-1  OO 
ON  M  tx       N  r^ 
r~.  O  "i       N  r>. 
O  I  «  ^^       |  N   M 

IS 

i| 

c 
.5 
"3 
« 

as 

6 
fe 

h"2   "22 
xx.xx 

ON  O    O  ^   t^  O 

OO  ^vO       vO  O 
w  o  r^      vo  O 

\O  w  ro       **  vd 

jj 

i 

ON  r^       ON  r^«  O 

•^  ON      VO  <->   w 

OO  VO         VO    L030 
>-    fOQ    f*>W?S 

CJ    Tf-^"    M    Tf  O 
n    ^          TfVO    M 

.1 

INI-^-     irof^oiw 

P 

(N      -^1               M     US     rH 

b'o      ^'oo 

If 

6 

?5 

XX     XXX 

too  ^  OO  r^  "^ 
r^       to  ON  to 
t^.        M    O   ** 
r^       to  M  ON 
t^        VO    "5f  ^O 

"-     N               M     Tj-   l-c 

c 

«J'E 

c  u 

1 

—         ro  N-   O   fO 
"">         O    t^  M    M 

«         f-O  ONX)   1-1 
OO  O  ^   ON  M  cxo 
i^w  to  r^  o  "•> 

t^         to  ON  M    r^ 

«         rodt«  M 

Revolutic 
per  min.,  pe 

d 

J5 

o     Mo     l"o 
X_,X     XX 

o  "  Q  O  tooo 

Q        0  ro  to  «-o 
Q         Q  ON  H-   ON 
O         O  Tf  ON  M 
O        O  to  to  t-** 

vd       c<S  oN  «  to 

t4 

%B 

|| 

J 

ON  »   O   ON  M 
^t  toc^  \o  r^ 
oo  «  oo  vo  ON 
Q  I-H  oo  "i  ro  ON 
w  M  r^»  O  N  t^ 
M  r^  N  -<f  ON 
IN  M|«|f')  d 

11 
H 
1 

d 

55 

T     7  T 
2222 
xxxx 

H  t^  Q  "^00  O 
\O   O  ™~>  "^  ro 

vo  O  «-"  N  ON 
vQ  O  ON  to  ^" 

VO    O    "TVO    »O 

«  vd  «  N  ON 

*o 
c 
o 

.« 

i 

OQ  O  fO  to  w 

ON  O4    N    N    t^ 

to  o   ro\O  ON 

rt  to  H«    1^\O  O 

2S83&2 

ioio6i4i«|d 

C                                         O 

Siderea 

6 
fc 

O   O   O   0   0 

XXXXX. 

ON  i--.  ro  I--  >-  H 

S  ^  #& 
?§*$? 

«  t^,  N  ON  - 

x 

S 

1 

tOCO    O    fO         t^ 
C-)     ^-  to  to          M 

VO   O   fOvO         O 
r^OO    -3-  O  O   ^ 
ON  to  i-   r-^        r^> 
ON  r^  fOOO        CO 
|M   N  vd   O\        ON 

Sidereal  I 

d 
55 

^^"2     2 
XXXX_,  X 

1^  ON  ON  *nH  vo 

rf  «-O  C4     M            ON 
VOOO    W    Tt-          ^t- 
Tj-  N  \Q    N          VO 
ON  r^  O    -^-        1^- 
O\  «-o  N  r>.       r>« 

•d 

c 

o 

! 

N  to  t-x       r^  "1 

tCN  ON       -^-  1^ 
ro\O         ro  fO 
t^.  fO.«.    ON  N 
.  OO    ^O    M    O 
«GO    "t          «    O 

idiooiTJ-      6  6 

1 

in 

c 

s 
X 

1 

lu  1 

XXX.  X 

i-c   vr»00  "    -^-OO 
<O    O   rv.        ON  ^t" 
ONO   1^       VD   "-> 
ro  «    t^        rj-  O 
f)  r^  t^       ro  O 
I-H   i^,  ri         w   w 

8 

3 
_C 

! 

>-o  r^»       n   O  t-> 
r^.  ON       O  IJ~>  r^ 

N  O         ro^O  vO 
ro  fOQ  O  "^00 
O  •<*•       tovo  ^n 
1  r^.1  -*•       roi  r^.  ro 

m 

|* 

4S 

ToTo     t'L'b 

| 

e 
B 

S 

d 
fe 

XX     XXX 

rOOO  H   O   t^  -* 
>-O  t^s.        O    ON  t^ 
M   r^       O  oo  ON 
N  r>-       O  ^  ^ 
oo  r^     vo  oo  vo 

rj-  N          ro  Tl-  fO 

M 

! 

1^          M    uo  M    O 

t^          O    O    "">00 

un       mvO   ON  O\ 
OO  'O   M   -   "* 
ro"  to  _   Tf  « 
rj        vo  H-   ri   w 

IfO       ror^tror^ 

1 

w 

a 
3 

41 

i 

o     'o'o  0*0 

XHXXXX 

vo         O  vO   "^  ^O 
rO        O   ON  -^  O 
r^      vo  f  »  r^  ro 

J          ro  M    J    M 

1 

! 

M  <-o  f-^  "~i  r< 

N    M    M    t^.  O 

"t1  r^  O   fO  ^ 
O  Q  vo  ro  M   LO 
^^  vO    <-    t-^Q  t^ 
t~^  fOOO   O  OO 
^^  vd  ^  O  ON 

Mean  Solar 

6 
55 

^22*2    *2 
XXX      X 

O   O  vo  OO  ON 
H   O  vo   ON  TfOO 
O   ro  rf  to  LO 
VO   t^vD   O    O 
r^  O   ^f  O  ^^ 

if^ti    t^.  «    t^ 

SMITHSONIAN  TABLES. 


18 


TABLES  20,  21 . 


CONVERSION    FACTORS. 


C 

i 

r^vo  ON  M  Ti- 
rj-  co  ON  O  co 

CO    C^    *-OvO  OO 

co  «">  co\o  -*O 
VO   io«  \o   O 
O  ^ot^oo  •<*• 

L 

•^•IN    OIN    O 

Centimetres  of 
at  o°  Cer 

o 
55 

ll  I 

XX     X 

r->  i^  ON  w  O  ^ 

CO  **    M    CO  O 

QQ     ^^     *•*     LO  O 

10  ON  r^  >-o  r^ 

>_i    vo  HI    CO  1O 

M  co  10  t^.  ri 

3 

1 

COf^    IOOO         VO 

«   o  vO  O       vO 
Q   "S"  t>.  l^»        « 
ON  O  00   i-  O  "^ 
xo^OO  vO  ^^   ON 

VO    «     CO  Tf           IO 

coirJ  6\n      l« 

EU 

1°° 
is 

.  y 

6 
8 

°"h     2     b 

XXXX 

O  vr>  ^  ONP^  "-< 
loco  ON  t^       O 
O   co  1O  "">        t^ 

vO   1-1    co  ON        co 
^o^  O  00        ON 

"ij-    M       W       W                   CO 

1 
|| 

! 

«-o  TJ-  r^       M  oo 
T  co  ON        COON 
M  vO   ON        N   co 
r^OO  vO  O  CO  co 
ONCO   Tf  w  co  co 
•"  vo  oo        "">  1-" 

ioi,j  ^     «« 

Ij 

'o  o  o      o  o 

1  5 

£  u 
£ 
O 

6 
SQ 

XXX     XX 

r^  i-  r^H  oo  vo 

OO    ^VO           N    >-O 
rj-  PJ    O           CO  ON 

r^co  co       >-o  10 
^ooo  O        -^  co 
~  TJ-  tA.       co  M 

g 

i 

a" 

i 

oo  r^       co  >-o  M 

^tco        0   COO 
P)  O         O   PI   •^> 

O  *•  O  co  1-1  vo 

iO  rf  ^    10  ONCO 

coco       -  v5  P) 
coico      iPil^iJ 

U4= 

a  % 

CO               G^     rH     i-H 

00         000 

"O 

1 

£ 

XX      XXX 

§Tj-PH     Tf   Tj-VO 
*T       PO  r>.  r^ 
^-          P)    w    CO 

Tf   Tf             PI     <->     CO 

Pi   ON       Tf  ON  ON 
pj  vd         iJ   Tf  •-! 

s 

1 

i 

1  1,^1! 

CO  O  °3    ^    ON  Tf 

O   ^     ^Ol-      Tf    Tf 

>-0        ^-    COX)   Tf 
10       ri   d  w  « 

Pounds  per 
foot. 

Q 

S5 

*O       ^O         O   O 

X      X      XX 

O  H   O    t^  O   <-< 
vO         O   '—i    ONVO 
iO         O  CO    PI    Tf 

P»               Tf    Tf    l^-OO 
PJ               Tf    O     O     t*» 

co       «  pJ  r^,  PI 

IJ 
il 

i 

ON  PI   >o  r^  co 
co  ">*OMJ  10 

cor-»  r^  ON  w 
Q    1-1    ON  PI    O  VO 

°     CNTf  0     TT  CO 

TfvO  OO   COON 
IvO  1  Tf  IvO  1  4-1  LO 

§s 
srii 

CD     •&      13      *^*     »O 

'o  'o  'o  'o  o 

S.1 
|l 

6 
% 

XXXXX 

H   ON  ON  co  Tf  co 
~   PI   r^  iv.co 

Q   Tf  ON  PI    PI 
O  vo   Tf  ON  co 

i-  Tf  co-  \q 

co  Tf  vd  PI  06 

MLVT3. 

L 

i 

i/-)  c)   »   M   ON 
rfCQ   c^vO   Tf 
O  vO   10  O  00 
„   O   PI   "">  «  Q 
oo  •'l-vo  r^  PI  w 
CO   «-    coco   P] 
vd   "f  N  vd   CO 

II 

S  8 
u  % 

<b"o<b<owo 

Dimensions 

Gramme 
per 

6 

£ 

XXXXX 

ro  "">  iO  Q  r^H 

tiOCN    O  VO 
OO    O   O  vO 
to  prji-ovo 

-v 

r>»  >-  M  r^  « 

1 

1 

CO 

£ 
«  . 
S  .<" 

i 

vo   co  PJ   co       •-« 
O  coco  w        «o 
*-  oo  vO  PI        ••* 
CNOO   O  POQ  °° 
un  -   TJ-  *ow  i^ 
vq  ON~VO        t^ 
co  dl"  co      |Tf 

1 

t 

5 

> 

3 

Kilogramme  ' 
per  minu 

0 

^ 

°2     bM2     2 
x    XXHX 

TJ-  ro  LO  Q         O 
M  i-o  n  o        o 

\O  ONOO  O        O 

IO  M    CO  LO         O 

rfod  H!  T}-    vo 

3 

f 

* 
| 

i 

TJ-  >-<  o        r^  ON 
00  M  r^      oo  ro 
C\^O   ^        t^  ON 
u->  10  r-^Q  vo  rt- 

Q  VO  CO           Tf  M 

O  N  "^      m  « 
difOl>o     l-^-l^. 

4 
3 
1 

3 

I 

I 

Force  de  ch 

0 

fc 

11   11 

XX     XX 

t^  o  «  "  <^  «o 

CO   ^t-  rt-        N   to 

CO  CO  O            M    CO 

>-<  n-  r^.       o  co 

o  oq  q      N  co 

w    w    CO          n    « 

$ 

3 
LI 

3 

I 

r  minute. 

i 

rj-  M           O  CO    ON 

(-1     LT)             CO  M      t^ 

to  M         »-n  co  •**• 

^^0  ^J  os^ 

»0t^        LOCO  O 

•^-  «       -^-  dico 

8 

| 

3 

i 

3 

K 
1 
1 

1 

0 

fc 

^  o     "o      o 
XX     X     X 

O  O         1-/P^  r^  Q 

O  O         ~3"  co  ON 
O   O         10  co  co 
CO  O           M    N    PO 

covd        cor^  •^> 

i 

| 

1 

t- 

3 

co       O\  O\^Q  ON 
vO         rj-  t^vO  >-> 
CO      CO   co  «   co 

^•°    N    COC2    ^ 

r^      M  j^  o  oo 

ri       |  N  c-i  |  «  Ito 

i 
i 

H 

• 

H 

Foot  Pounds  pe 

i 

"2    V^V'2 
x    xxxx 

O  ^   r^-  «-O  O   O 

O       ^   t^  *-o  o 
O       \O   rf  >-O  co 
O        O   M   O   co 

LO          VQ     Tf    W     N 

10       i-J  10  w  rA. 

iS 

! 

r^\O  vD  rf  10 
coco  -  0  »o 
\O  ^  O  co  ON 
O   CN-H    rf  000 
**   LOOO   ON  TT  « 

C)     Tf  QN   CO  I-J 

I  col  vru  «  |  TJ-I  f^ 

a 

Vo'ol'o 

K 

o 

fe 

XXXXX 

H  oo  O  ON  c>  ON 

N-    CO  *^  CO    O 

^2^^o\^ 

oq  o  oq  «  co 

i--    CO  O\  f-l    w 

SMITHSONIAN  TABLES. 


TABLES  22,  23. 


CONVERSION   FACTORS. 


i 

timetres. 

i 

O    N    N    Tf  0 

fO«  CO  00   Q 
ON  t^»vo  LO  O  _ 
o  >H   O  LO  Q  O 

ON  Tf  Tf-  ON  O 

Tf    Tf    M      N      O 

Dimensions  =: 

Gramme  Cen 

d 

ft 

22^2    '°2 

XXX      X 

CJNVO  GO   r^*-  O 

row 

"5 

i 

O    Cl    N    Tf          O 

row  GO  OO         O 
ON  Tf  Tf  ON        O 

I 
3 

d 

1-H      10                Ui 

22^2     2 

XXXX      X 

»-H   o  LO  r>»^   O 

ON  M    LOO           O 

vo  LO  N   LO       O 

ONVO  oo  r-^       O 
q  r^.  rpON       q 

i 

VO  OO  OO        VO  vO 

Tf    N      ON              1-H      M 

row   O         Tf  Tf 
LOVO   LOQ   Tf  Tf 

HH  i-i  oo        r^  r^» 

c 

r^  tv.  ro       Tf  I  w 

6 

tbtbco      'b  b 

§ 

d 

XXXHXX 

4 

1 

cT  O5       ON  ro  ro 
rp  rp'      «  00  CO 

Foot  Pour 

d 

22    \    \ 

XX     X      X 

O   O  '*   ^"  O   Q 

Tt"  O            W    CO  CO 

il 

i 

CO           O    M  CO  CO 
t-4           t^x  t^^CO  OO 

OQ  c»  ^ooo  co 
C?       !  -4-lo6  1  fOloo 

Foot  Toi 
(One  ton  —  20 

d 

ft 

T  T  T  T 

0    0   0   O 

HXXXX 

O         O  00   LO  10 

A 

bio 

r-)   M   Tf  O   O 
co  LO  LO  t^.  r>. 

r^  r^O   O   Q 
Q   O   ON  rf  ON  ON 
LO  Tf  o    O    O 

1  ^  i  Tf  106  1  fO'oo 

IFoot  To 
(One  ton  =  »2 

d 

XXXXX 
rH  r^  ON  LO  M  N 
"  LOM  LOO   Q 
CO  rf  t-^  ON  ON 

M  VO    £.  M    N 

O     M      Tf 

LO  ro  ro 

\ 

cf 

^^^o 

^ 

^ 

J 

I^LOO  ° 

H.      N      Tf 

II 

c 

c 

HH      N|M 

Dimensio 

•ammes  per 
centimetr 

22*2 
XXX 

O 

i 

vO   ON  ro 

CO    LO  M 

CO  00    LO 

g1 

r^co       vo 

ON  0s      ^ 
LO  LOQ  ro 

•g 

3 

VO    Tfv    ON 

.S 

1 

rTS       ^ 

R, 

"22        2 

c 
're 

HO 

XX     X 

O 

* 

ro8        00° 

roO         ON 

co  q       q\ 

LO  r>.       ro 

ON       r-i  oo 

i 

M         o  vO 
CO         ON^ 

I 

c 

C7N        HH    t^ 

c 

IL 

;  U 

c 

3 
O 

d 
ft 

X      XX 

ro1""'   TfvO 

fi 

ro      CO   ON 
ro        ri   ON 

ro        rf  LO 

CO           i-'    LO 

•-,   roON 

| 

1 

r^  ro  c< 

q  N  co 

|| 

S 

.s 

K 

«  » 

000 

1 

d 

XXX 

(2 

""ill 

SMITHSONIAN  TABLES. 


20 


CONVERSION   FACTORS. 


TABLES  24,  25, 


i 

i 

QNw    t-i    rf 

&  r^t^co 

ON  N    N    ON 

r^  ro  ro  >OQ 
vo  f*")  CO  Q 

•j 

IHH 

1 

111 

4 

d 

XXX     _, 

u 

u 

£ 

r"1 

1 

vo  •—  '    H-I  OO 

b 

cT  s^voir 

£«  ^  « 

»o  t-^  i-x      vo 

^^^S      S 

i 

I 

ON  N  ri        o 
£o£r  C4  O  ON 

u 

h*ldl*  l« 

^ 

VO    S     CO             ^. 

d 

E 

o  o  o      o 

a 
1 

6 
fc 

XXXHX 

r^vo  vo        ON 

M    vo  vo         — 

X 

10,4  «        cK 

i 

vq  q      oq  oq 

|N|«C.          N    N 

j 

I 

U    "2^ 

6 
fc 

XX     XX 

ro  O  ""^  vO   O 
0   0         ^ovn 

M    O           vo  IO 

3-2    itS 

oo       o  fo  o 

ON       O   «   en 

i 

1 

vo        O  r^  r^ 

^f  Q   O    N  vO 

vq       q  oq  oq 

o 

LO       r^  o  ON 

II 

Q    D 

'S     'o'o'o 

£S 

1 

c 

6 

X     XXX 

fOrH   O  vo   O 
O         O   vo  vo 
Tt-       O  O\  r^ 

3 

1    §S2 

i 

i_ 

i 

N    N    vo  w 
0    0    -    fO 
roro  O   O 

O    "">  V000    N 

ro  f*5  «  N 

N*~   *4 

l 

T 

1 

XXXX 

£ 

1 

1 

H  N   N   ro  vo 

S&aS 

u, 

ro  to  r>*  t^N, 

f{    «|   M    M 

SMITHSONIAN  TABLES. 


i 


XXXX 

VO   ro  fO  vo 

VOON  ON  N 


r-x  ON  ON      00 

rovO  vo  fO 
N  t^.  r^O  ON 
ONVO  vo  ^^  >0 

•*o   o        o 


bbb         b 

XXX     X 


;<=>COON 

hH       ON 


t 

O 


T  T 
o  o 

XX 


o  g       MO 

!§  ??i 

•4"  M  l-I    ON 


XXX 

O   ONO 
O  vo  O 


to  w 

boob 
XXXX 


ro  moo  r^ 
ro  CON   ro 

N    N    CO  N 


21 


TABLES  26,  27. 


CONVERSION    FACTORS. 


5 

^ 

ji 

<? 

f  I!0 

s 

1 

14 

«"  roq 

II 

§ 

o 

•a 

? 

S 

si 

T     T 

1 

w 

bob 

Q 

s 

d 

XXX 

M 

% 

\O   *-o  O  ^" 

^^8 

M    44    M 

c? 

l-So  1 

J 

J 

§s°i 

§ 

0 

rt 

r-               Cl 

1 

XX      X 

d 

1 

% 

CO    ci          0 

Q 

o 

~    ri         M 

re  inch. 

1 

%     co"^o" 

vO         ON  ON 

\%           •     - 
1  to      1  "^T"!  W 

5 

1 

& 

To     ToTo 

1 

d 

X      XX 

§ 

fe 

5     v^-v^- 

is  vis 

vd         Tt-^- 

N    OS  OS 

j 

1 

^cocc 

••* 

w  In  O 

5 

1 

1 

01 

0) 

a, 

2  2 

1 

XX 

a 

d 

,    O    i—  i    i—  i 

1 

fc 

O   ON  ON 

a 

i 

Iff0 

li 

8.S. 

«     Cjl 

i  E 

0   0 

|! 

d 

XX 

i 

CO    OSM 
Tf"  i—  <     ^O 

.  8 

rC     W 

C  O- 

i 

vo  r^      vo 

r4-  CS        VO 
Tf  "1          M 

=0^6      o 

i| 

d 
fc 

XX      X 
it  ON     ^ 

c5 

>-<   OS        Os 

per  linear  cm. 

i 

oo       m  os 

^        Ovo 

OO           T^"VO 

ro      |w   ci 

•b     Vo 

R 

d 

XH  XX 

rt-        O    - 

to       rj  os 

| 
I 

i 

M  VO    « 

to  ^^  ^  i 

i-    tocO 

Q   ^-  n   to 
vO  vo  to' 

CJ  VO    M 

0    0    0 

I 

. 

XXX 

§ 

% 

H    ^CO^ 

c?2^co 

SMITHSONIAN  TABLES. 


22 


TABLES  28,  29. 


CONVERSION    FACTORS, 


per  cubic  centim. 

i 

IvHl 

11  ol 

1 

o 

XXXX 

E 

X 

Tf   Tf   CNiO   " 

1 

C^vS^  C> 
ri   «   ci   ro 

1 

M 

rO  Tf  CO           Tf 

vo  vr>  o         ON 
O  i^  Lr>Q  H 

£84   1 

3 
O 

too  O   ro       r^ 

"           e^           <N 
O         O         O 

c 

c 

0 

0 

XXX 

LO  ro  Q  ^   "-1 
O   ^  O         O^ 
Tf  0   O        CO 

O    "">  O            M 
vo  O    O           *O 

1 

bb 

o 

CO   "">        Q  ro 

LOTf           ONOO 

vo  ci  -^   Tf  r^^ 

ONVO  O    vo  vo 

oo  r^       «  vo 

.y 

J3 

3 

s 

|N|Tf         |Tf|N 

lTo      11 

Pounds 

1 

XX_,XX 

ro  Tf  "">   r^  Tf 
ON  O         vo  r^ 
c»   r^      co   M 

rC,  vo       w  ro 

r  cubic  foot. 

i 

oo         Tf  vO   O 

n             Tf   Tf  CO 

i-         vo  Tf  ro 
ro®   ro  ON  ON 

bo        rni«  ^ 

°o     'b'b'b 

? 

6 

X      XXX 

c 

^H 

n  r*l   o  i^  ^^ 

1 

CO         OO  OO    M 
VO          C)  VO    Tf 

«         ^   ri  vd 

r  cubic  mile. 
nds=  i  ton. 

i 

c-^  u**>  i^»  c^ 
r^  ^   H-  u-i 

00    rl-  ro  M 

O  *O    O    ^ovD 
r^  HN   f^  ON 

'b'o  'o^o 

°  8 

6 

XXXX 

ON    KH    VO      Tf 

VO  F^  tan    ON 

co  ri  oq  LO 

O  ^j£ 

8.§ 


rt  E 

C 

o  c 


a 


i-  00   O   O 

O  vo  O   O 

vo  N   H   « 


XXXX 

I" 


i 


q     oq 

I    M  |  VO 


•b  o     "b 
XX      X 

crf^.8Hca 


CO  O 
CN  r<~) 
V2  - 


Vb     Uo 

XX      XX 
oo  pj  H  oco 

Tf  en         O    CN 


VOQ  CO  00    ro 

n       co  co   rv. 


'.^  c^     -r    oo 

2     222 
X      XXX 


N   0  !«! 


X 

H   r 


XX 


^^cfc? 

®88^ 


SMITHSONIAN  TABLES. 


TABLES  30,  31. 


CONVERSION    FACTORS, 


*$* 

d 

J 

ONVO  OO  O 

.5 
g 

•iSJSiS* 

I 

8 

eo   <H    <M 

| 

000 

1 

3 

51 

xxx_, 

to  CO  O  ""» 

ON  ON  O 

second. 

* 

X/-)  xy1^          QQ 

OO  OO          N 
IN    O          M 

1 

b         2 

o 

* 

11 

* 

10       00    to 

O          *^"  to 

coo  «  H 

•"^ 

C\        »-*    ro 

«j 

I  to      !  w   O 

3 

C 

i 

CO              rH 

O         O 

1 

0 

£H^ 

ft    3,8 

oo       «  N 

r^  n  M 

s 

°C^I 

1 

«4      NH      C-3 

i. 

°b  o5© 

•3 

XXX 

o 

Hv£c78 

Co  co  M 

EM 

ft 

lij 


-  a 

'rt    bfi 

E-8 


SO 


i! 

US 


i 


i 


XX 

M    N  \O  H 

VO  ^O   co 


VO 

00 
""> 


2     22 
X     XX 


XXX 

H  ovo  co 

O   "—    CO 


SMITHSONIAN  TABLES. 


TABLES  32,  33, 


CONVERSION    FACTORS. 


TABLE  32.  — Conversion  Factors  lor  Expression  of  Temperatures. 


Dimension  =  0. 


Centigrade. 

Fahrenheit.* 

Reaumur. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

1 

5-55556  X  lo-1 

1.25000 

0 

1.744727 

0.096910 

1.80000 
1 
2.25000 

0.255272 
0.352182 

8.00000  X  io~l 
4.44444  X  lo-1 

1.903090 

1.647817 
0 

The  zero  of  the  Fahrenheit  scale  is  32°  below  the  freezing  point  of  water. 


In  many  of  the  derived  units  for  the  measurement  of  physical  quantities,  the 
unit  of  time  may  be  taken  as  constant,  because  it  is  seldom  that  any  other  unit 
than  the  second  is  used.  This  is  the  case,  in  particular,  for  the  electric  and 
magnetic  units.  Tables  33-37  below,  giving  the  factors  for  the  conversion  of 
units  depending  on  different  dimensional  equations  in  M  and  L  from  one  set 
of  fundamental  units  to  another,  will  be  found  sufficient  for  almost  all  cases. 


TABLE  33.  —  Electric  Displacement,  etc. 


Dimensions  =  M*L  *T". 


Foot  Grain 
Second  Units. 

Metre  Gramme 
Second  Units. 

Centimetre  Gramme  or  )  Second 
Millimetre  Milligramme  J  Units. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

1 
6.61058  X  lo-1 
6.61058  X  ic2 

0 

1.820240 
2.820240 

1.51273 

i.ooooo  X  io3 

0.179760 
0 
3.000000 

i.  51273  X  io~3 
i.ooooo  X  io~3 

1 

3.179760 

3-000000 

0 

SMITHSONIAN  TABLES. 


TABLES  34,  35. 


CONVERSION   FACTORS, 


i-' 

4> 

s 
1 

i 

ill- 

"s 

n' 

WJ.t! 

0    «    N 

c 
o 

Ii 

22 

5 

ejj 

XX 

I 

.5 

6 

S 

1 

^ 

^§  8 

^22 

S§    § 

1 

1 

I 

00         8 

Eg 

1  N  1  1-N         Id 

5 

°£ 

VI      r-l                O^ 

1         1 

• 

i  § 

00         0 

& 

E  u 

6 

XX     X 

•s 

U 

^ 

^8H  8 

>i 

o  o      o 

1 

is   s 

1 

•a  §§ 

1 

J 

\o      o  o 

I 

£2 

|«                 M|« 

i 

E'S 

" 

sl 

2     22 

S 

ll 

6 

X     XX 

o      o  o 

4-      w  w 

* 

Ol  m 

<» 

?l?ll? 

!1 

2^2 

o  3 

—  5 

XX 

6 

C?>  00  OO 

00  CO  CO 
O  ^O  vO 

E-c 


E'S 

v:^ 


6^ 

l§ 
C/3 


ll 


XX 


SMITHSONIAN   TABLES. 


TABLES  36,  37 


CONVERSION   FACTORS. 


1 

II 


c/3 


II 

i"§ 

£  8 


LI 


1 


XXX 


« 


vq  q 


22     2 
XX     X 


fO 


X     XX 


XXX 

ON  ON  ON 


SMITHSONIAN  TABLES. 


y 


H 

1 

II 


i 


i 


<&: 


'S  2*2 
XXX 

"^"  O  Q  i 

^8  8 
&8§ 


<&: 


$ 


05  T 

HM     NH  H4 

XX     X 

3!H§ 

ft§    8 


oo 

° 


2    Ts 

X     XX 

vO        O  O 


<=> 


XXX 
,0?^ 


TABLE  38. 


HYPERBOLIC  FUNCTIONS.* 


Hyperbolic  sines. 


Values  of 


00 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

0.0000 

O.OIOO 

O.O2OO 

0.0300 

0.0400 

0.0500 

0.0600 

0.0701 

0.0801 

0.0901 

O.I 

.1002 

.1102 

.I2O3 

.1304 

.1405 

.1506 

.1607 

.1708 

.1810 

.1911 

O.2 

.2013 

.2115 

.2218 

.2320 

.2423 

.2526 

.2629 

•2733 

.2837 

.2941 

•S^0 

•3255 

•336o 

.3466 

•3572 

.3678 

•3785 

.3892 

.4000 

0.4 

.4108 

.42?6 

•4325 

•4434 

•4543 

•4653 

.4764 

•4875 

.4986 

.5098 

0.5 

0.5211 

0-5324 

0.5438 

0.5552 

0.5666 

0.5782 

0.5897 

0.6014 

0.6131 

0.6248 

0.6 
°-7 

.6367 

.7586 

.6485 
.7712 

.6605 
•7838 

.6725 
.7966 

.6846 
.8094 

.6967 
.8223 

.7090 
•8353 

•7213 

.8484 

•7336 
.8615 

.7461 

'  .8748 

0.8 

.8881 

.9015 

.9150 

.9286 

•9423 

.9561 

.9700 

.9840 

.9981 

.0122 

0.9 

1.0265 

1.0409 

1-0554 

1.0700 

1.0847 

1.0995 

1.1144 

1.1294 

1.1446 

1.1598 

1.0 

1.1752 

1.1907 

1.2063 

I.222O 

1-2379 

1-2539 

1.2700 

1.2862 

1.3025 

1.3190 

i.i 

•3356 

•3524 

•3693 

•3863 

•4035 

.4208 

.4382 

.4558 

•4735 

.4914 

.2 

•5095 

.5276 

•5460 

•5645 

•5831 

.6019 

.6209 

.6400 

•6593 

.6788 

•3 

.6984 

.7182 

•7583 

.7786 

.7991 

.8198 

.8406 

.8617 

.8829 

•4 

.9043 

•9259 

•9477 

.9697 

.9919 

2.0143 

2.0369 

2.0597 

2.0827 

2.1059 

1.5 

2.1293 

2-1529 

2.1768 

2.2008 

2.2251 

2.2496 

2.2743 

2-2993 

2.3245 

2.3499 

.6 

•3756 

.4015 

.4276 

•4540 

.4806 

•5075 

•5346 

.5620 

.5896 

.6i75 

•7 

.6456 

.6740 

.7027 

•73I7 

.7609 

•79°4 

.8202 

•8503 

.8806 

.9112 

.8 

.9422 

•9734 

3.0049 

3.0367 

3.0689 

3-IOI3 

3-I34Q 

3.1671 

3-2005 

3-234I 

•9 

3.2682 

3-3025 

•3372 

.3722 

•4075 

•4432 

.4792 

•5X56 

•5523 

.5894 

2.0 

3.6269 

3-6647 

3.7028 

3-74I4 

3-7803 

3.8196 

3-8593 

3-8993 

3-9398 

3.9806 

2.1 

4.0219 

4-0635 

4.1056 

4.1480 

4.1909 

4.2342 

4.2779 

4.3221 

4.3666 

4.4117 

2.2 

4-4571 

4-5030 

4-5494 

4.5962 

4.6434 

4.6912 

4-7394 

4.7880 

4-8372 

4.8868 

2-3 

4-9370 

4.9876 

5-0387 

5-0903 

5^425 

5-I95I 

5-2483 

5.3020 

5.3562 

5.4109 

2.4 

5.4662 

5-5221 

5-5785 

5-6354 

5.6929 

5-75io 

5.8097 

5.8689 

5.9288 

5.9892 

2.5 

6.0502 

6.1118 

6.1741 

6.2369 

6.3004 

6.3645 

6.4293 

6.4946 

6.5607 

6.6274 

2.6 

6.6947 

6.7628 

6.8315 

6.9009 

6.9709 

7.0417 

7.1132 

7-1854 

7-2583 

7.3319 

2.7 

7.4063 

7.4814 

7.5572 

7-6338 

7.7112 

7.7894 

7-8683 

7.9480 

8.0285 

8.1098 

2.8 

8.1919 

8.2749 

8.3586 

8.4432 

8.5287 

8.6150 

8.7021 

8.7902 

8.8791 

8.9689 

2.9 

9.0596 

9-1512 

9-2437 

9-3371 

9-43I5 

9.5268 

9.6231 

9.7203 

9.8185 

9-9I77 

3.0 

10.018 

10.119 

IO.22I 

10.324 

11.429 

11  -534 

11.640 

11.748 

11.856 

11.966 

3-1 

11.076 

11.188 

11.301 

11.415 

11.530 

12.647 

12.764 

12.883 

1  2.003 

12.124 

3-2 

12.246 

12.369 

12.494 

12.620 

12.747 

12.876 

13.006 

I3-I37 

13.269 

^3-403 

3-3 

13-538 

13-674 

13.812 

'3-951 

14.092 

14-234 

14-377 

14.522 

14.668 

14,816 

3-4 

14.965 

15.116 

15.268 

15.422 

15-577 

1  5-734 

I5-893 

16.053 

16.214 

16.378 

3.5 

16.543 

16.709 

16.877 

17.047 

17.219 

I7-392 

I7-567 

17-744 

17-923 

18.103 

3-6 

18.285 

18.470 

18.655 

18.843 

1  9-033 

19.224 

19.418 

19.613 

19.811 

2O.OIO 

3-7 

2O.2II 

20.415 

2O.62O 

20.828 

21.037 

21.249 

21.463 

21.679 

21.897 

22.117 

3-8 

22.339 

22.564 

22.791 

23.020 

23.252 

23.486 

23.722 

23.961 

24.202 

24-445 

3-9 

24.939 

25.190 

25.444 

25.700 

25-958 

26.219 

26.483 

26.749 

27.018 

4.0 

27.290 

27.564 

27.842 

28.122 

28.404 

28.690 

28.979 

29.270 

29.564 

29.862 

4-i 

3O.l62 

30-465 

30.772 

31.081 

31.393 

3J-709 

32.028 

32-350 

32-675 

33-004 

4.2 
4-3 

36.843 

33-67I 
37-214 

37.'588 

34-351 
37.966 

34.697 
38-347 

35-046 
38.733 

35-398 
39.122 

35-754 
39-5*5 

36.113 

40.314 

4-4 

40.719 

41.129 

41.542 

41.960 

42.382 

42.808 

43-673 

44.112 

44-555 

4.5 

45-003 

45-455 

45.912 

46.374 

46.840 

47-311 

47787 

48.267 

48-752 

49.242 

4.6 

4-7 
4.8 

49-737 
54.969 
60.751 

50-237 
55.5" 
61.362 

50.742 
56.080 
61.979 

51-252 
56-643 
62.601 

5^767 
57-213 
63-231 

52.288 
57.788 
63.866 

52.813 

58-369 
64.508 

53-344 
58.955 
65-1  57 

53.880 
59-548 
65.812 

54422 
60.147 
66.473 

4-9 

67.141 

67.816 

68.498 

69.186 

69.882 

70.584 

7I-293 

72.010 

72.734 

73-465 

*  Tables  38-41  are  quoted  from  "  Des  Ingenieurs  Taschenbuch,' 
SMITHSONIAN  TABLES. 

28 


herausgegeben  vom  Akademischen  Verein  (Hiitte). 


HYPERBOLIC  FUNCTIONS. 

Hyperbolic  cosines.  Values  of 


TABLE  39. 


X 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

1.  0000 

1.  000  1 

1.0002 

1.0005 

1.0008 

1.0013 

1.0018 

1.0025 

1.0032 

1.0041 

O.I 

.0050 

.0061 

.OO72 

.0085 

.0098 

.0113 

.0128 

.0145 

.0162 

.0181 

0.2 

.0201 

.0221 

.0243 

.0266 

.0289 

.0314 

.0340 

-0367 

•°395 

.0423 

o-3 

•0453 

.0484 

.0516 

-0549 

.0584 

.0619 

.0655 

.0692 

-0731 

.0770 

0.4 

.0811 

.0852 

-0895 

•0939 

.0984 

.1030 

.1077 

.1125 

.1174 

.1225 

0.5 

1.1276 

1.1329 

I-I383 

1.1438 

'  I-M94 

1.1551 

1.1609 

1.1669 

1.1730 

1.1792 

0.6 

•1855 

.1919 

.1984 

.2051 

.2119 

.2188 

.2258 

•2330 

.2402 

.2476 

0.7 

•2552 

.2628 

.2706 

•2785 

.2865 

•2947 

-3030 

•3IJ4 

•3»99 

.3286 

0.8 

•3374 

•3464 

•3555 

•3647 

•3740 

-3835 

•3932 

.4029 

.4128 

.4229 

0.9 

•4331 

4434 

•4539 

-4645 

•4753 

.4862 

•4973 

•5085 

•5!99 

•5314 

1.0 

I-543I 

1-5549 

1.5669 

1-5790 

I-59I3 

1.6038 

.6164 

1.6292 

1.6421 

1.6552 

.1 

.6685 

.6820 

.6956 

•7093 

•7233 

•7374 

•75*7 

.7662 

.7808 

•7956 

.2 

.8107 

.8258 

.8412 

.8568 

.8725 

.8884 

.9045 

.9208 

•9373 

•9540 

•3 

.9709 

.9880 

2.0053 

2.0228 

2.0404 

2-0583 

2.0764 

2.0947 

2.1132 

2.1320 

•4 

2.1509 

.1700 

.1894 

.2090 

.2288 

.2488 

.2691 

.2896 

•33!  2 

1.5 

2-3524 

2.3738 

2-3955 

2.4174 

2-4395 

2.4619 

2.4845 

2-5073 

2-5305 

2.5538 

.6 

•5775 

•6013 

•6255 

.6499 

.6746 

.6995 

•7247 

.7502 

.7760 

.8020 

•7 

.8283 

.8549 

.8818 

.9090 

•9364 

.9642 

.9922 

3.0206 

3.0492 

3.0782 

.8 

3-1075 

3.1669 

3.2277 

3-2585 

3.2897 

.3212 

•3530 

•3852 

1.9 

•4177 

.4506 

.4838 

•5173 

.5512 

•5855 

.6201 

.6904 

.7261 

2.0 

3.7622 

37987 

3-8355 

3-8727 

3-9103 

3-9483 

3.9867 

4-0255 

4.0647 

4.1043 

2.1 

4-1443 

4.1847 

4.2256 

4.2668 

4-3085 

4.3507 

4-3932 

4.4362 

4-4797 

4.5236 

2.2 

4-5679 

4.6127 

4.6580 

47037 

4.7499 

4.7966 

4.8437 

4.8914 

4-9395 

4.9881 

2-3 

5-0372 

5.0868 

5-I37° 

5.1876 

5.2388 

5.2905 

5-3427 

5-3954 

5.4487 

5-5026 

2.4 

5.6119 

5.6674 

57235 

5.7801 

5-8373 

5-895  ' 

5-9535 

6.0125 

6.0721 

2.5 

6.1323 

6.1931 

6-2545 

6.3166 

6-3793 

6.4426 

6.5066 

6.5712 

6.6365 

6.7024 

2.6 

2-7 

6.7690 

7-4735 

6.8363 
7-5479 

6.9043 
7.6231 

6.9729 
7.6990 

7.0423 

7-7758 

7.1123 

7.1831 
7-9!36 

7.2546 
7.0106 

7.3268 
8.0905 

7-3998 
8.1712 

2.8 

8-2527 

8-3351 

8.4182 

8.5022 

8.5871 

8.6728 

8.7  594 

8.8469 

8-9352 

9.0244 

2.9 

9.1146 

9.2056 

9.2976 

9-3905 

9.4844 

9-579! 

9-6749 

9.7716 

9.8693 

9.9680 

3.0 

10.068 

10.168 

10.270 

10-373 

10.476 

10.581 

10.687 

10.794 

10.902 

II.OII 

3-1 

II.  121 

12.233 

11  -345 

n-459 

n-574 

11.689 

1  1.  806 

11.925 

12.044 

12.165 

3-2 

12.287 

13.410 

12.534 

12.660 

12.786 

12.915 

13.044 

13.175 

I3-307 

13.440 

3-3 
3-4 

13-575 
14.999 

14.711 

13.848 
15-301 

13-987 
1  5-455 

14.127 
15.610 

14.269 
15.766 

14.412 
15.924 

14-556 
16.084 

14.702 
16.245 

14.850 
16.408 

3.5 

16.573 

16.739 

16.907 

17.077 

17.248 

17.421 

I7-596 

17.772 

!7.95i 

18.131 

3-6 

18.313 

18.497 

18.682 

18.870 

19.059 

19.250 

19-444 

19.639 

19.836 

20.035 

3-7 

20.236 

20.439 

20.644 

20.852 

21.061 

21.272 

21.486 

21.702 

21.919 

22.139 

3-8 

22.362 

22.586 

22.813 

23.042 

23-273 

23-507 

23-743 

23.982 

24.222 

24.466 

3-9 

24.711 

24-959 

25.210 

25.463 

25.719 

25-977 

26.238 

26.502 

26.768 

27.037 

4.0 

27.308 

27.582 

27.860 

28.139 

28.422 

28.707 

28.996 

29.287 

29.581 

29.878 

4.1 
4.2 
4-3 
4-4 

30.178 
33-351 
36-857 
40-732 

30.482 
33-686 
37.227 
41.141 

30.788 
34.024 
37.601 
41-554 

31.097 
34-366 

37-979 
41.972 

31.409 
34-7" 
38-360 
42.393 

31725 
35.060 
38.746 
42.819 

32.044 
35-412 
39-135 

43-250 

35768 
43-684 

32.691 
36.127 

39-925 
44-123 

33019 
36.490 
40.326 
44.566 

4.5 

4.6 

4-7 
4.8 

45.014 
49-747 
54-978 
60.759 

45-466 

50.247 

55-531 
61.370 

45-923 
50-752 
56.089 
61.987 

46.385 
51.262 
56.652 
62.609 

46.851 

5'-777 
57.221 

47-321 
52.297 

57-796 
63.874 

47-797 

52.823 

58-377 
64.516 

48.277 

53-354 
58.964 
65.164 

48.762 
53-890 
59-556 
65-819 

49.252 
54.431 

60.155 

66.481 

4-9 

67.149 

67.823 

68.505 

69.193 

69.889 

70-591 

71.300 

72.017 

72.741 

73-472 

SMITHSONIAN   TABLES. 


29 


TABLE  40. 


HYPERBOLIC   FUNCTIONS. 

Common  logarithms  +  10  of  the  hyperbolic  sines. 


X 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

8.  

oooo 

3011 

4772 

6022 

6992 

7784 

8455 

9036 

9548 

O.I 

0007 

0423 

0802 

1152 

1475 

1777 

2060 

2325 

2576 

2814 

0.2 

3°39 

3254 

3459 

3656 

3844 

4025 

4199 

4366 

4528 

4685 

0-3 
0.4 

4836 
9.6136 

4983 

6249 

5125 
635; 

5264 
6468 

5398 
6574 

5529 
6678 

5656 
6780 

578i 
6880 

5902^ 
6978 

6020 
7074 

t 

0.5 

9.7169 

7262 

7354 

7444 

7533 

7620 

7707 

7791 

7875 

7958 

0.6 

8039 

8119 

8199 

8277 

8354 

843  r 

8506 

8581 

8655 

£728 

0.7 

8800 

8872 

8942 

9012 

9082 

9150 

9218 

9286 

9353 

2412 

0.8 

9485 

9550 

9614 

9678 

9742 

9805 

9868 

9930 

9992 

°°53 

0.9 

10.0114 

0174 

0234 

0294 

0353 

0412 

0470 

0529 

0586 

0644 

1.0 

10.0701 

0758 

0815 

0871 

0927 

0982 

1038 

1093 

1148 

1203 

i.i 

1257 

1311 

1365 

1419 

1472 

1525 

1578 

1631 

1684 

1736 

1.2 

1788 

1840 

1892 

1944 

1995 

2046 

2098 

2148 

2199 

2250 

1-3 

1.4 

2300 
2797 

2351 
2846 

2401 
2895 

2451 
2944 

2501 
2993 

255i 

2600 
3090 

2650 
3138 

2699 
3186 

2748 
3234 

1.5 

10.3282 

3330 

3378 

3426 

3474 

3521 

3569 

3616 

3663 

37n 

1.6 

3758 

3805 

3852 

3899 

3946 

3992 

4039 

4086 

4132 

4T79 

i-7 

4225 

4272 

4318 

4364 

4411 

4457 

45°3 

4549 

4595 

4641 

1.8 

4687 

4733 

4778 

4824 

4870 

4915 

4961 

5°°7 

5052 

5098 

1.9 

5J43 

5188 

5234 

5279 

5324 

5370 

5415 

5460 

55°5 

5550 

2.0 

2.1 

iQ-5595 
6044 

5640 
6089 

5685 
6134 

5730 
6178 

5775 
6223 

5820 
6268 

5865 
6312 

5910 

5955 
6401 

6446 

2.2 

6491 

6535 

6580 

6624 

6668 

6713 

6757 

6802 

6846 

6890 

2-3 

6935 

6979 

7023 

7067 

7112 

7200 

7244 

7289 

7333 

2.4 

7377 

7421 

7465 

7509 

7553 

7597 

7642 

7686 

773° 

7774 

2.5 

10.7818 

7862 

7906 

7994 

8038 

8082 

8126 

8169 

8213 

2.6 

8257 

8301 

8345 

8433 

8477 

8521 

8564 

8608 

8652 

2-7- 

8696 

8740 

8784 

. 

8871 

8915 

8950 

9^03 

9046 

9090 

2.8 

9^4 

9178 

9221 

9265 

9309 

9353 

9396 

9440 

9484 

9527 

2.9 

957i 

9615 

9658 

9702 

9746 

9789 

9833 

9877 

9920 

9964 

3.0 

11.0008 
0444 

0051 
0488 

0095 

°53  l 

0139 

°575 

0182 
0618 

0226 
0662 

0270 
0706 

0313 
0749 

°357 
°793 

0400 
0836 

3-2 

0880 

0923 

0967 

IOII 

1054 

1098 

1141 

1185 

1272 

3-3 

1316 

T359 

1403 

1446 

1490 

»533 

1577 

1620 

1664 

1707 

3-4 

1751 

1794 

1838 

1881 

J925 

1968 

2012 

2056 

2099 

2143 

3.5 

11.2186 

2230 

2273 

2317 

2360 

2404 

2447 

2491 

2534 

2578 

3-6 

2621 

2665 

2708 

2752 

2795 

2839 

2882 

2925 

2969 

3012 

3-7 

3056 

3°99 

3*43 

3186 

3230 

3273 

3317 

3360 

3404 

3447 

3-8 

349  i 

3534 

3578 

3621 

3665 

3708 

3752 

3795 

3838 

3882 

3-9 

3925 

3969 

4012 

4056 

4099 

4H3 

4186 

4230 

4273 

4317 

4.0 

11.4360 

4403 

4447 

449° 

4534 

4577 

4621 

4664 

4708 

4751 

4.1 

4795 

4838 

4881 

4925 

4968 

5012 

5055 

5099 

5186 

4.2 

5229 

5273 

53l6 

5359 

5403 

5446 

5490 

5533 

5577 

5620 

4-3 
4.4 

5664 
6098 

5707 
6141 

575° 
6185 

5794 
6228 

5837 
6272 

5881 
6315 

5924 
6359 

5968 
6402 

6011 
6446 

6489 

4.5 

11  ^532 

6576 

6619 

6663 

6706 

6750 

6793 

6836 

6880 

6923 

4.6 

6967 

7010 

7054 

7097 

7141 

7184 

7227 

7271 

73*4 

7358 

4-7 

7401 

7445 

7488 

7531 

7575 

7618 

7662 

7705 

7749 

7792 

4.8 
4-9 

7836 
8270 

7879 
8313 

7922 
8357 

7966 
8400 

8009 
8444 

8053 
8487 

8096 
8530 

8140 
8574 

8183 
8617 

8226 
8661 

SMITHSONIAN  TABLES. 


HYPERBOLIC   FUNCTIONS. 

Common  logarithms  of  the  hyperbolic  cosines. 


TABLE  41 


* 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

o.oooo 

oooo 

0001 

OOO2 

0003 

0005 

0008 

001  1 

0014 

0018 

O.I 

OO22 

0026 

0031 

0037 

0042 

0049 

0055 

0062 

0070 

0078 

0.2 

0086 

0095 

0104 

OII4 

0124 

0134 

0145 

0156 

0168 

0180 

0.3 

0193 

0205 

0219 

0232 

0246 

0261 

0276 

0291 

0306 

0322 

0.4 

0339 

0355 

0372 

0390 

0407 

0426 

0444 

0463 

0482 

0502 

0.5 

O.O522 

0542 

0562 

0583 

0605 

0626 

0648 

0670 

0693 

0716 

0.6 

0739 

0762 

0786 

0810 

0835 

0859 

0884 

0910 

°935 

0961 

o-7 

0987 

1013 

1040 

1067 

1094 

1122 

1149 

1177 

1206 

1234 

0.8 

1263 

1292 

1321 

1350 

1380 

I4IO 

1440 

1470 

1501 

1532 

0.9 

1563 

1594 

1625 

1657 

1689 

1721 

1753 

1785 

1818 

1851 

1.0 

0.1884 

1917 

'95° 

I984 

2018 

2051 

2086 

2I2O 

2154 

2189 

i.i 

2223 

2258 

2293 

2328 

2364 

2399 

2435 

2470 

2506 

2542 

1.2 

2578 

2615 

2651 

2688 

2724 

2761 

2798 

2835 

2872 

2909 

I-3 

2947 

2984 

3022 

3°59 

3°97 

3135 

3173 

32II 

3249 

3288 

1.4 

3326 

3365 

3403 

3442 

348i 

3559 

3598 

3637 

3676 

1.5 

0-37I5 

3754 

3794 

3833 

3873 

3913 

3952 

3992 

4032 

4072 

1.6 

4112 

4192 

4232 

4273 

4313 

4353 

4394 

4434 

4475 

1.7 

45T5 

4556 

4597 

4637 

4678 

47  19 

4760 

4801 

4842 

4883 

1.8 

4924 

4965 

5006 

5048 

5089 

5*3° 

5172 

5213 

5254 

5296 

1.9 

5337 

5379 

5421 

5462 

5504 

5545 

5587 

5629 

5671 

5713 

2.0 

0-5754 

5796 

5838 

5880 

5922 

5964 

6006 

6048 

6090 

6132 

2.1 

6217 

6259 

6301 

6343 

6386 

6428 

64/0 

6512 

6555 

6597 

6640 

6682 

6724 

6767 

6809 

6852 

6894 

6937 

6979 

2-3 

2.4 

7022 
7448 

7064 

7107 
7534 

7150 

7577 

7192 
7619 

7J35 
7662 

7278 
7705 

7320 
7748 

7363  . 
7791 

7406 
7833 

2.5 

2.6 

0.7876 
830; 

7919 
8348 

7962 
8391 

8005 
8434 

8048 
8477 

8091 

8520 

8134 
8563 

8176 
8606 

8219 
8649 

8262 
8692 

2-7 

8731 

8778 

8821 

8864 

8907 

8951 

8994 

9037 

9080 

9123 

2.8 

2.9 

9166 
9597 

9209 
9641 

9252 
9684 

9295 
9727 

9338 
9770 

9382 
9813 

9856 

9468 
9900 

9511 
9943 

9554 
9986 

3.0 

1.0029 

0073 

0116 

0159 

O2O2 

0245 

0289 

0332 

0375 

0418 

3-1 

0462 

°5°5 

0548 

0591 

0635 

0678 

0721 

0764 

0808 

0851 

3-2 
3-3 
3-4 

0894 
1327 
1761 

0938 
1804 

0981 
1414 
1847 

1024 

H57 
1891 

1067 
I5OI 

mi 

1544 
1977 

1154 
1587 
202  1 

1197 
2064 

1241 

1674 
2107 

1284 
1717 
2151 

3.5 

1.2194 

2237 

2281 

2324 

2367 

2411 

2454 

2497 

2541 

2584 

3-6 

2628 
3061 

2671 
3I05 

2714 

2758 

2801 

2844 
3278 

3322 

2931 
3365 

2974 
3408 

3018 
3452 

3-9 

3495 
3929 

3538 
3972 

3582 
4016 

3625 
4059 

4103 

3712 
4146 

3755 
4189 

3799 
4233 

3842 
4278 

3886 
4320 

4.0 

4.1 
4-2 
4-3 
4-4 

1-4363 

4797 

6099 

4406 
4840 
5274 
5709 
6143 

445° 
4884 
5318 

4493 
4927 

5795 
6230 

4537 

5f5 
5839 
6273 

4580 
5014 
5448 
5882 
6316 

4623 
5°57 
5492 
5926 
6360 

4667 
5101 
5535 
5969 
6403 

4710 
5M4 
5578 
6012 
6447 

4754 
5188 
5622 
6056 
6490 

4.5 

1.6533 

6577 

6620 

6664 

6707 

6751 

6794 

6837 

6881 

6924 

4.6 

4-7 
4.8 

4-9 

6968 
7402 
7836 
8270 

7011 

7445 
7880 

8314 

7055 
7489 
7923 
8357 

7098 

7532 
7966 
8401 

7141 
7576 
8010 
8444 

7185 
7619 

8053 
8487 

7228 
7662 
8097 
8531 

7272 
7706 
8140 
8574 

73i5 
7749 
8184 
8618 

7358 
7793 
8227 
8661 

SMITHSONIAN  TABLES. 


TABLE  42. 


EXPONENTIAL    FUNCTIONS. 


Values  of  *•*  and  of  e-*  and  their  logarithms. 


Values  of  B*  and  e~*  for  values  of  x  intermediate  to  those  here  givet 
values  of  the  hyperbolic  cosine  and  sine  given  in  Tables  38-39. 


may  be  found  by  adding  or  subtracting  the 


(0 

ex 

^ 

X 

* 

,og. 

x. 

ri 

log,, 

0.1 

.1052 

0.04343 

5.1 

164.03 

2.21490 

0.1 

0.90484 

1.95657 

2 

.2214 

08686 

2 

181.27 

25833 

2 

81873 

9I3I4 

3 

•3499 

13029 

3 

200.34 

30176 

3 

74082 

86971 

4 

.4918 

17372 

4 

221.41 

345  '9 

4 

67032 

82628 

5 

.6487 

21715 

5 

244.69 

38862 

5 

60653 

78285 

0.6 

1.8221 

0.26058 

5.6 

270.43 

2.43205 

0.6 

0.54881 

7.73942 

7 

2.0138 

30401 

7 

298.87 

47548 

7 

49659 

69599 

8 

2.2255 

34744 

8 

330-30 

51891 

8 

44933 

65256 

9 

2.4596 

39087 

9 

365-04 

56234 

9 

40657 

60913 

I.O 

2.7183 

43429 

6.0 

40343 

60577 

I.O 

36788 

56570 

1.1 

3.0042 

0.47772 

6.1 

445-86 

2.64920 

1.1 

0.33287 

1.52228 

2 

3.3201 

52H5 

2 

492-75 

69263 

2 

30119 

47885 

3 

3.6693 

56458 

3 

545-57 

736o6 

3 

27253 

43542 

4 

4-0552 

60801 

4 

601.85 

77948 

4 

24660 

39  199 

5 

4.4817 

65U4 

5 

665.14 

82291 

5 

22313 

34856 

1.6 

4-9530 

0.69487 

6.6 

735-io 

2.86634 

1.6 

0.20190 

1.30513 

7 

5-4739 

7383° 

7 

812.41 

90977 

7 

18268 

26170 

8 

6.0496 

78173 

8 

897-85 

95320 

8 

16530 

21827 

9 

6.6859 

82516 

9 

992.27 

99663 

9 

M957 

17484 

2.O 

7.389' 

86859 

7-o 

1096.63 

3.04006 

2.O 

'3534 

'3*4i 

2.1 

8.1662 

0.91202 

7.1 

I2I2.0 

3-o8349 

2.1 

0.12246 

1.08798 

2 

9.0250 

95545 

2 

1339-4 

12692 

2 

1  1  080 

04455 

3 

9.9742 

99888 

3 

1480.3 

17035 

3 

10626 

OOII2 

4 

11.0232 

1.04231 

4 

1636.0 

21378 

4 

09073 

2-95/69 

5 

12.1825 

08574 

5 

1  808.0 

25721 

5 

08208 

91426 

2.6 

13.463 

1.12917 

7.6 

1998.2 

3.30064 

2.6 

0.074274  * 

2.87083 

8 

14.880 
16.445 

17260 
21602 

8 

2208.3 
2440.6 

34407 
38750 

8 

067205 
060810 

82740 
78398 

9 

18.174 
20.086 

25945 
30288 

si 

2697.3 
2981.0 

43°93 
47436 

^9 

055023 
049787 

74055 
69712 

3.1 

22.198 

1-34631 

81 

3294.5 

3-5r779 

3.1 

0.045049 

2.65369 

2 

24.533 

38974 

2 

3641.0 

56121 

2 

040762 

61026 

3 

27.113 

433  1  7 

3 

4023.9 

60464 

3 

036883 

156683 

4 

29.964 

47660 

4 

4447.1 

64807 

4 

033373 

52340 

5 

33-115 

52003 

5 

4914.8 

69150 

5 

030197 

47997 

3.6 

7 

36.598 
40.447 

1.56346 
60689 

8.6 

5431-7 
6002.9 

3-73493 
77836 

3.6 

7 

0.027324 
024724 

243654 
393  ri 

8 

44.701 

65032 

8 

6634-2 

82179 

8 

022371 

34968 

9 
4.0 

49.402 
54.598 

69375 
737i8 

9 
9.0 

7332-0 
8103.1 

86=522 
90865 

9 

4.0 

020242 
018316 

30625 
26282 

4.1 

60.340 

1.78061 

9.1 

8955- 

3.95208 

4.1 

0.016573 

2.21939 

2 

66.686 

82404 

2 

9897. 

995  5  i 

2 

014996 

1/596 

3 

73.700 

86747 

3 

10938. 

4.03894 

3 

013569 

13253 

4 

81.451 

91090 

4 

I  2088. 

08237 

4 

012277 

08910 

5 

90.017 

95433 

5 

13360. 

12580 

5 

011109 

04567 

4.6 

99.48 

'•99775 

96 

14765. 

4.16923 

4.6 

0.010052 

2.00225 

7 

109.95 

2.04118 

7 

16318. 

21266 

7 

009095 

3.95882 

8 

•121.51 

08461 

8 

18034. 

25609 

8 

008230 

9*539 

9 

134.29 

12804 

9 

19930. 

29952 

9 

007447 

87196 

5-o 

148.41  / 

17147 

IO.O 

22026. 

34295 

S-o 

006738 

82853 

SMITHSONIAN  TABLES. 


EXPONENTIAL   FUNCTIONS. 

Value  of  e*2  and  e-*2  and  their  logarithms. 


TABLE  43. 


The  equation  to  the  probability  curve  isy  —  e~x*,  where  x  may  have  any  value,  positive  or 
•negative,  between  zero  and  infinity. 


0 

0* 

log  *** 

e-x* 

log  e-x* 

0.1 

I.OIOI 

0.00434 

0.99005 

1.99566 

2 

1  .0408 

01737 

96079 

98263 

3 

1.0904 

03909 

91393 

96091 

4 

i-!735 

06949 

85214 

93°5  r 

5 

1.2840 

10857 

77880 

89M3 

0.6 

M333 

0.15635 

0.69768 

1.84365 

7 

1.6323 

21280 

61263 

78720 

8 

1.8965 

27795 

52729 

72205 

9 

2.2479 

35*78 

44486 

64822 

1.0 

2.7183 

43429 

36788 

56571 

1.1 

2 

3-3535 
4.2207 

0.52550 

62538 

0.29820 
23693 

1.47450 
37462 

3 

54195 

73396 

18452 

26604 

4 

7.0993 

85122 

14086 

14878 

5 

9.4877 

97716 

10540 

02284 

1.6 

1.2936  X  10 

1.  11179 

0.77306  X  JO"1 

5.88821 

7 

1.7993   " 

25511 

55576    " 

74489 

8 

2-5534   " 

40711 

39l64 

59289 

9 

3.6996   " 

56780 

27052 

43220 

2.O 

5-4598 

73718 

18316 

26282 

2.1 

8.2269 

1.91524 

0.12155   " 

2.08476 

2 

1.2647  X  io2 

2.10199 

79070  X  io~2 

3.89801 

3 

1.9834 

29742 

50418   " 

70258 

4 

3-1735 

50154 

315"  ;' 

49846 

5 

5.1802 

7J434 

19304 

28566 

2.6 

8.6264   " 

2.93583 

0.11592  " 

3.06417 

7 

1.4656  X  io3 

3.16601 

68233  X  io~3 

4.83400 

8 

2.5402   " 

40487 

39367 

595J3 

9 

4.4918 

65242 

22263   «• 

34758 

3-o 

8.1031 

90865 

12341 

09135 

3.1 

1.4913  X  io* 

4-17357 

0.67055  X  io~4 

5.82643 

2 

3 

2.8001 
5.2960 

44718 
72947 

35713 
18644   " 

55283 
27053 

4 

1.0482  X  io5 

5.02044 

95402  X  io~5 

6.97956 

5 

2.0898 

32011 

47851 

67989 

3.6 

4-2507 

5.62846 

0.23526   «« 

6.37154 

8 

8.8205   " 
1.8673  X  io6 

94549 
6.27121 

11  337 
53554  X  io-« 

_  05451 
7.72879 

9 

4.0329   " 

60562 

24796 

3943s 

4.0 

8.8861 

94871 

11254 

05129 

4.1 

1.9976  X  io7 

7.30049 

0.50062  X  io~" 

5.69951 

2 

3 

4.5809   " 
1.0718  X  io8 

8.0301  1 

21829 

93303  X  10-8 

339°5 
9.96989 

4 

2-5583   " 

40796 

39088 

59204 

5 

6.2297 

79447 

16052   " 

20553 

4.6 

8 

i.  5476  X  io9 
3.9228 
1.0143  X  io10 

9.18967 

59357 
10.00615 

0.64614  X  io~9 

25494 

98595  X  io-10 

75.81033 
40643 
ii-99385 

9 

2-6755   " 

42741 

37376 

57259 

5-o 

7.2005 

85736 

13888   " 

14264 

SMITHSONIAN  TABLES. 


33 


TABLE  44. 


EXPONENTIAL    FUNCTIONS. 

ff  —  -X 

Values  of  i*  t*&6     4   and  their  logarithms. 


* 

IT 

log  e^* 

*-T* 

IT 

log  &     * 

1 

2-!933 

0.34109 

0-45594 

1.65891 

2 

3 

4.8105 
1.0551  X  io 

.68219 
1.02328 

.20788 

.94780  X  io-1 

.31781 
2.97672 

4 

2.3141 

•36438 

.43214 

.63562 

5 

5-0754 

.70547 

•19703 

•29453 

6 

1.1132  X  io2 

2.04656 

0.89833  X  IO-2 

3.95344 

7 

2.4415 

.38766 

.40958     " 

.61234 

8 

5-3549       " 

•72875 

.18674 

..27125 

9 

10 

1.1745  X  io3 
2.5760 

3.06985 
.41094 

.85144  X  10-3 

.38820     " 

4-9301  5 
.58906 

11 

12 

5.6498       " 
1.2392  X  io4 

3-75204 

4-093  !  3 

0.17700       " 
.80699  X  io-4 

4-24796 
5.90687 

13 

2.7168 

•43422 

•36794 

•56578 

14 

5.9610 

•77532 

.16776    " 

.22468 

1.3074  X  io5 

5.11641 

.76487  X  io~5 

6.88359 

16 

2.8675       " 

5-45751 

0.34873     " 

6.54249 

17 

6.2893       " 

.79860 

.15900 

.20140 

i8 

1.3794  X  io6 

6.13969 

.72495  X  IO-6 

7.86031 

19 

3-o254 

.48079 

•33053 

.51921 

20 

6.6356 

.82189 

.15070 

.17812 

TABLE  45. 


EXPONENTIAL  FUNCTIONS. 

Values  of  &~**  and  6     *~*  and  their  logarithms. 


X 

V* 

e  * 

V* 

log  e~^x 

r-*- 

V? 

log  e    • 

1 

1.4429 

0.19244 

0.64203 

1.80756 

2 

2.4260 

.38488 

.41221 

.61512 

3 

3-7786 

•57733 

.26465 

.42267 

4 

•     5.8853 

•76977 

.16992 

•23023 

5 

9.1666 

.96221 

.10909 

•03/79 

6 

14.277 

1-15465 

0.070041 

2-84535 

7 

22.238 

•34709 

.044968 

.65291 

8 

34-636 

•53953 

.028871 

.46047 

9 

53-948 

•73198 

.018536 

.26802 

10 

84.027 

.92442 

.011901 

•07558 

11 

130.87 

2.11686 

0.0076408 

3-88314 

12 

203.85 

•30930 

.0049057 

.69070 

13 

3!7-5o 

•5OI74 

.0031496 

.49826 

H 

494.52 

.69418 

.0020222 

.30582 

15 

770.24 

.88663 

.0012983 

•"337 

16 

1199.7 

3.07907 

0.00083355 

4.92093 

17 

1868.5 

.27151 

•00053517 

•72849 

18 

2910.4 

•46395 

.00034360 

•53605 

J9 

4533-1 

•65639 

.OOO22O6O 

•34361 

20 

7060.5 

.84883 

.00014163 

•IS*1? 

SMITHSONIAN  TABLES. 


34 


EXPONENTIAL   FUNCTIONS. 

Value  of  e*  and  e~*  and  their  logarithms. 


TABLE  46. 


. 

e* 

log  e* 

e~ 

log  e—  * 

i/64 

1.0157 

0.00679 

0.98450 

1.99321 

1/32 

•0317   ' 
.0645 

-OI357 
.02714 

.96923 
•93941 

.98643 
.97286 

I/IO 

.1052 

•04343 

•95657 

1/9 

•1175 

.04825 

.89484 

.95175 

1/8 

1.1331 

0.05429 

0.88250 

i"-9457i 

1/7 

•1536 

.06204 

.86688 

•93796 

SUI    S 

i/6 

.1814 

.07238 

.84648 

.92762 

i/  5 

.2214 

.08686 

.81873 

-9*3*4 

T/4 

.2840 

.10857 

.77880 

.89143 

1/3 

I-3956 

0.14476 

0.71653 

1.85524 

1/2 

.6487 

.21715 

.60653 

•78285 

3/4 

2.1170 

•32572 

•47237 

.67428 

i 

•7183 

.43429 

.36788 

•56571 

5/4 

3-4903 

•54287 

.28650 

•45713 

3/2 

4.4817 

0.65144 

0.22313 

1.34856 

7/4 

5-7546 

.76002 

•17377 

•23998 

2 

7.3891 

.86859 

•T3535 

.13141 

9/4 

9.4877 

.97716 

.10540 

.02284 

5/2 

12.1825 

1.08574 

.08208 

2.91426 

LEAST  SQUARES.* 

Values  of  P  =  —=.  j    '*«-(**>  X 


TABLE  47. 


This  table  gives  the  value  of  P,  the  probability  of  an  observational  error  having  a  value  positive  or  negative  equal 
to  or  less  than  x  when  h  is  the  measu 


measure  of  precision,  P  =r  -.-^  i        e—  (hx)* 

Jo 


hx 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0.0 

O.I 

.01128 
.12362 

.02256 
•13476 

•03384 
•14587 

.04511 
•15695 

•05637 
.16800 

.06762 
.17901 

.07886 
.18999 

.09008 
.20094 

.10128 
.21184 

.11246 
.22270 

O.2 

•23352 

.24430 

•25502 

.26570 

•27633 

.28690 

.29742 

.30788 

.31828 

.32863 

o-3 
0.4 

•33891 
•43797 

•34913 
•44747 

•35928 
.45689 

.36936 
.88623 

•37938 
•47548 

•38933 
.48466 

•33921 
•49375 

.40901 

•50275 

.41874 
.51167 

•42839 
•52050 

0.5 

0.6 

•52924 
.61168 

•53790 
.61941 

.54646 
.62705 

•55494 
•63459 

•56332 
.64203 

.57162 
•64938 

•57982 
.65663 

.58792 
.66378 

•59594 
.67084 

.60386 
.67780 

u 

.68467 
.74800 

.69143 
•7538i 

.69810 
•75952 

.70468 
.76514 

.71116 

.77067 

•7I754 
.77610 

.72382 
.78144 

.73001 
.78669 

.73610 
.79184 

.74210 
.79691 

0.9 

.80188 

.80677 

.81156 

.81627 

.82089 

.82542 

.82987 

•83423 

•83851 

.84270 

1.0 

.84681 

.85084 

.85478 

.85865 

.86244 

.86614 

.86977 

•87333 

.87680 

.88020 

i.i 

.88353 

.88679 

.88997 

.89308 

.8961  2 

.89910 

.90200 

.90484 

.90761 

.91031 

1.2 

.91296 

•9J553 

.91805 

.92051 

.92290 

.92524 

-92751 

•92973 

.93190 

•93401 

1.4 

.93606 
•95385 

•93807 
•9553s 

.94001 
.95686 

.94191 
•95830 

•94376 
•95970 

•94556 
.96105 

•94731 
.96237 

.94902 
•96365 

.96490 

.95229 
.96610 

1.5 

1.6 

.96728 
.97721 

.96841 
.97804 

•96952 

.97884 

•97059 
.97962 

.97162 

.98038 

.97263 
.98110 

.97360 
.98181 

•97455 
.98249 

•97546 
•983  *  5 

.97635 
.98379 

3 

.98441 
.98952 

.98500 
.98994 

•98558 
•99035 

.98613 
•99074 

.98667 
.99111 

.98719 
.99147 

.98769 
.99182 

.98817 
.99216 

.98864 
.99248 

.98909 
.99279 

1.9 

•99309 

•99338 

•99366 

.99392 

.99418 

•99443 

.99466 

.99489 

•99511 

•99532 

*  Tables  47-52  are  for  the  most  part  quoted  from  Howe's  "  Formulas  and  Methods  used  in  the  application  of  Least 

Squares." 

SMITHSONIAN  TABLES. 

35 


TABLE  48. 


LEAST  SQUARES. 


This  table  gives  the  values  of  the  probability  P,  as  defined  in  last  table,  corresponding  to  different  values  of 
x I  r  where  r  is  the  "  probable  error."     The  probable  error  r  is  equal  to  0.476947  h. 


as 

T 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

.00000 

.00538 

.01076 

.01614 

.02512 

.02690 

.03228 

.03766 

•04303 

.04840 

O.I 

•05378 

.05914 

.06451 

.06987 

•07523 

.08059 

•08594 

.09129 

•09663 

.10197 

0.2 

.10731 

.11264 

.11796 

.12328 

.12860 

I3391 

.13921 

•I4451 

.14980 

•15508 

o-3 

.16035 

.16562 

.17088 

.17614 

.18138 

.18662 

.19185 

.19707 

.20229 

.20749 

0.4 

.21268 

.21787 

.22304 

.22821 

.23336 

•23851 

•24364 

.24876 

.25388 

.25898 

0.5 

.26407 

.26915 

.27421 

.27927 

.28431 

.28934 

.29436 

•29936 

•30435 

•30933 

0.6 

•3I43° 

•3J925 

.32419 

.32911 

•33402 

•33892 

•3438o 

.34866 

•35352 

•35835 

0.7 

•363  1  7 

.36798 

.37277 

•37755 

•38231 

•38705 

•39^78 

•39649 

.40118 

.40586 

0.8 

.41052 

.4i5J7 

.41979 

.42440 

.42899 

•43357 

43813 

.44267 

.44719 

.45169 

0.9 

.45618 

.46064 

.46509 

.46952 

•47393 

•47832 

.48270 

48605 

•49!39 

•49570 

1.0 

i.i 

.50000 
.54188 

.50428 
•54595 

•50853 
.55001 

•5I277 
.55404 

.51699 
•55806 

.52119 

.56205 

•52537 
.56602 

•52952 
•56998 

.53366 
•57391 

•53778 
•57782 

1.2 

.3 

.58171 
.61942 

.58558 
.62308 

.62671 

•59325 
.63032 

•59705 
•6339  l 

.60083 
•63747 

.60460 
.64102 

.60833 
•64554 

.61205 
.64804 

.61575 
•65152 

•4 

.65498 

.65841 

.66182 

.66521 

.66858 

•67193 

.67526 

.67856 

.68184 

.68510 

1.5 

.68833 

•69*55 

.69474 

.69791 

.70106 

.70419 

.70729 

.71038 

.71344 

.71648 

.6 

.71949 

.72249 

.72546 

.72841 

•73T34 

•73425 

•73714 

.74000 

•74285 

•74567 

.7 

.74847 

•75I24 

•75400 

•75674 

•75945 

.76214 

.76481 

•76746 

.77009 

.77270 

.8 

.77528 

•77785 

.78039 

.78291 

•78542 

.78790 

•79036 

.79280 

•79522 

.7976i 

•9 

•79999 

•80235 

.80469 

.80700 

.80930 

.81158 

•81383 

.81607 

.81828 

.82048 

2.0 

.82266 

.82481 

.82695 

.82907 

.83117 

•83324 

•8353° 

•83734 

•83936 

•84137 

2.1 

2.2 

•84335 
.86216 

•84531 
.86394 

.84726 
•86570 

.84919 

.86745 

.85109 
.8691  7 

.85298 
.87088 

.85486 
•87258 

.85671 
•87425 

•85854 
•87591 

.86036 

•87755 

!  2.3 

.87918 

.88078 

.88237 

.88395 

.88550 

.88705 

•88857 

.89008 

•89^57 

.89304 

2.4 

.89450 

•89595 

.89738 

.89879 

.90019 

•90157 

.90293 

.90428 

.90562 

.90694 

2.5 

.90825 

•90954 

.91082 

.91208 

•9T332 

.91456 

•91578 

.91698 

.91817 

•9*935 

2.6 

.92051 

.92166 

.92280 

.92392 

•92503 

.92613 

.92721 

.92828 

•92934 

•93038 

2.7 

•93  HI 

•93243 

•93344 

•93443 

•93541 

•93638 

•93734 

.93828 

.93922 

.94014 

2.8 

.94105 

•94195 

.94284 

•94371 

.94458 

•94543 

.94627 

•947  1  1 

•94793 

.94874 

2.9 

•94954 

•95°33 

.95111 

•95*87 

.95263 

•95338 

.95412 

•95484 

•95557 

.95628 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

3 

.95698 

.96346 

.96910 

•97397 

.97817 

.98176 

.98482 

•98743 

.98962 

.99147 

4 

.99302 

•9943  i 

•99539 

99627 

.99700 

.99760 

.90808 

.99848 

•99879 

•99905 

5 

.99926 

•99943 

.99956 

.99966 

•99974 

.99980 

.99985 

.99988 

.99991 

•99993 

LEAST  SQUARES. 

Values  of  the  factor  0.6745\/-^_ . 
\»i— 1 

This  factor  occurs  in  the  equation  eg  =  0,6745^!  —^   for  the  probable  error  of  a  single  observation,  and  other 

similar  equations. 


n    = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

0.6745 

0.4769 

0.3894 

0-3372 

0.3016 

0.2754 

0.2549 

0.2385 

10 

0.2248 

0.2133 

.2029 

.1947 

.1871 

.1803 

.1742 

.1686 

.1636 

.1590 

20 

•IS47 

.1508 

'  -1472 

.1438 

.1406 

•1377 

•J349 

•1323 

.1298 

•1275 

30 

.1252 

.1231 

.1211 

.1192 

.1174 

•"57 

.1140 

.1124 

.1109 

.1094 

40 

.1080 

.1066 

•1053 

.1041 

.1029 

.1017 

.1005 

.0994 

.0984 

.0974 

50 

0.0964 

0.0954 

0.0944 

0-0935 

0.0926 

0.0918 

0.0909 

0.0901 

0.0893 

0.0886 

60 

.0878 

.0871 

.0864 

•0857 

.0850 

•0843 

.0837 

.0830 

.0824 

.0818 

,  70 

.0812 

.0806 

.O8OO 

•0795 

.0789 

.0784 

•0778 

•0773 

.0768 

.0763 

80 

•0759 

•0754 

.0749 

•0745 

.0940 

.0736 

•0731 

.0727 

.0723 

.0719 

90 

•0715 

.0711 

.0707 

.0703 

.0699 

.0696 

.0692 

.0688 

.0685 

.0681 

SMITHSONIAN  TABLES. 


LEAST  SQUARES. 

Values  of  the  factor  0.6745\/ 
\ 


TABLE  5O 


_  , 
n(n—  1)' 


This  factor  occurs  in  the  equation  em  =  o.674$\  for  the  probable  error  of  the  arithmetic  mean, 

\'  n(n — i) 


n   = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

10 

0.07  1  1 

0.0643 

0.4769 

.0587 

0.2754 
.0540 

0.1947 
.0500 

0.1508 
.0465 

0.1231 

•°435 

0.1041 
.0409 

0.0901 
.0386 

0.0795 
•°365 

20 

.0346 

.0329 

.0314 

.0300 

.0287 

.0275 

.0265 

.0255 

.0245 

.0237 

30 

40 
50 

0.0229 
.0171 
.0136 

O.O22I 
.0167 
.0134 

0.0214 
.0163 
.0131 

0.0208 
.0159 
.0128 

O.O2OI 

•0155 
.0126 

0.0196 
.0152 
.0124 

0.0190 
.0148 
.0122 

0.0185 
.0145 
.0119 

0.0180 
.0142 
.0117 

0.0175 
.0139 
.0115 

LEAST  SQUARES. 

Values  of  the  factor  0.8453\/ — 

\n(» 


TABLE  51. 


This  factor  occurs  in  the  equation  es  —  0.8453-^  •  for  the  probable  error  of  a  single  observation. 

»  H\n — ij  • 


n   = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

0.5978 

0-3451 

0.2440 

0.1890 

0-1543 

0.1304 

0.1130 

0.0996 

10 

0.0891 

0.0806 

.0736 

.0677 

.0627 

.0583 

.0546 

•°5r3 

.0483 

•0457 

20 

•0434 

.0412 

•0393 

.0376 

.0360 

•0345 

•0332 

.0319 

.0307 

.0297 

30 

0.0287 

0.0277 

0.0268 

0.0260 

0.0252 

0.0245 

0.0238 

0.0232 

0.0225 

O.O22O 

40 

.0214 

.0209 

.0204 

.0199 

.0194 

.0190 

.0186 

.0182 

.0178 

.0174 

50 

.0171 

.0167 

.0164 

.0161 

.0158 

•oi55 

.0152 

.0150 

.0147 

.0145 

( 

LEAST  SQUARES, 

Values  of  0.8453      1 


TABLE  52, 


This  table  gives  the  average  error  of  the  arithmetic  mean  when  the  probable  error  is  one. 


n   = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

0.4227 

0.1993 

O.I  22O 

0.0845 

0.0630 

0.0493 

0.0399 

0.0332 

IO 

20 

0.0282 
.0097 

0.0243 
.0090 

.0212 
.0084 

.0188 
.0078 

.0167 

.0073 

.0151 
.0069 

.0136 
.0065 

.0124 
.0061 

.0144 
.0058 

.0105 
•0055 

30 

40 
5° 

0.0052 
-,0034 
.0024 

0.0050 
•0033 
.0023 

0.0047 
.0031 
.0023 

0.0045 
.0030 

.0022 

0.0043 
.0029 

.0022 

0.0041 
.0028 
.0021 

0.0040 
.0027 
.0020 

0.0038 
.0027 

.0020 

0.0037 
.0026 
.0019 

0.0035 
.0025 
.0019 

SMITHSONIAN  TABLES. 


37 


TABLE  53. 


GAMMA   FUNCTION.* 


Value  of  log 


•JT 


r 

ion)    I 

Jo 


Values  of  the  logarithms  +  10  of  the  "  Second  Eulerian  Integral "  (Gamma  function) 

for  values  of  «  between  i  and  2.     When  n  has  values  not  lying  between  i  and  2  the  value  of  the  function  can  be 
readily  calculated  from  the  equation  T(n-{-i)  —  nT(rt)  =  n(n—i)  .   .  .  (« — r)T(n — r). 


n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1.00 

9-99  

97497 

95001 

92512 

90030 

S7555 

85087 

82627 

80173 

77727 

I.OI 

75287 

72855 

7043° 

68011 

65600 

63196 

60799 

58408 

56025 

53648 

i.  02 

51279 

48916 

46561 

44212 

41870 

39535 

37207 

34886 

32572 

30265 

1.03 
1.04 

27964 
05334 

25671 
03108 

23384 
00889 

ml 

18831 
96471 

16564 
94273 

^ 

12052 
89895 

li?5 

07567 
55544 

1.05 

9-9883379 

81220 

79068 

76922 

74783 

72651 

70525 

68406 

66294 

64188 

i.  06 

62089 

59996 

579*0 

55830 

53757 

51690 

49630 

47577 

45530 

43489 

1.07 

41469 

39428 

37407 

35392 

33384 

31382 

29387 

27398 

25415 

23449 

i.  08 
1.09 

21469 
02123 

19506 
00223 

17542 
98329 

96442 

^3655 

11717 
92686 

07860 
89856 

25241 
87100 

04029 
85250 

1.10 

9.9783407 

81570 

7973s 

779*4 

76095 

74283 

72476 

70676 

68882 

67095 

i.  ii 

65313 

63538 

61768 

60005 

58248 

56497 

54753 

53OI4 

51281 

49555 

1.  12 

47834 

46120 

44411 

42709 

41013 

39323 

37638 

3596o 

34288 

32622 

I.I3 

30962 

29308 

27659 

26017 

24381 

22751 

21126 

19508 

17896 

16289 

I.I4 

I4689 

13094 

09922 

08345 

06774 

05209 

03650 

02096 

00549 

1.15 

9.9699007 

97471 

9591  1 

94417 

92898 

91386 

89879 

88378 

86883 

85393 

1.16 

83910 

82432 

80960 

79493 

78033 

76578 

75I29 

73686 

72248 

70816 

1.17 

6939° 

67969 

66554 

D545 

63742 

62344 

60952 

59566 

58185 

56810 

1.18 

55440 

54076 

52718 

51366 

50019 

48677 

46011 

44867 

43368 

1.19 

42054 

40746 

39444 

36856 

35570 

34290 

33016 

3*747 

30483 

1.20 

9.9629225 

27973 

26725 

25484 

24248 

23017 

21792 

20573 

*935S 

18150 

1.  21 

16946 

15748 

*4556 

13369 

12188 

I  IOI  I 

0984  r 

0867.5 

2Z515 

06361 

1.22 

05212 

04068 

02930 

01796 

00669 

99546 

98430 

97318 

96212 

951  *  * 

1.23 

594015 

92925 

91840 

90760 

89685 

88616 

87553 

86494 

85441 

84393 

1.24 

83350 

82313 

81280 

80253 

79232 

78215 

77204 

76198 

75*97 

74201 

1.25 

.26 

•27 

63592 

54487 

72226 
62658 
53604 

71246 
61730 

52727 

70271 
60806 
5^55 

69301 
59888 
50988 

68337 

58975 
50126 

67377 
58067 
49268 

66423 
57165 
48416 

65474 
56267 
47570 

64530 
55374 
46728 

.28 

4589f 

45059 

44232 

42593 

41782 

40975 

40173 

39376 

38585 

.29 

3779s 

37016 

36239 

35467 

34700 

33938 

32439 

31682 

30940 

1.30 

9.9530203 

29470 

28743 

28021 

27303 

26590 

25883 

25180 

24482 

23/89 

.31 

23100 

22417 

21739 

21065 

20396 

19732 

19073 

18419 

17770 

17125 

•32 

16485 

15850 

15220 

14595 

13975 

13359 

!2748 

12142 

11540 

10944 

•33 

K>353 

09766 

09184 

08606 

08034 

07466 

06903 

06344 

0579* 

05242 

•34 

04698 

04158 

03624 

03094 

02568 

02048 

OI532 

OIO2I 

00514 

00012 

1.35 

9-94995  T  5 

99023 

98535 

98052 

97573 

97100 

96630 

96166 

95706 

95251 

•36 

94800 

94355 

93913 

93477 

93°44 

92617 

92194 

91776 

91362 

90953 

•37 

90549 

90149 

89754 

89363 

88977 

88595 

88218 

87846 

87478 

87II5 

•38 

86756 

86402 

86052 

85707 

85366 

85030 

84698 

843"1 

84049 

83731 

•39 

83417 

83108 

82803 

82503 

82208 

81916 

81630 

81348 

81070 

80797 

1.40 

9.9480528 

80263 

80003 

79748 

79497 

79250 

79008 

78770 

78537 

78308 

.41 

78084 

77864 

77648 

77437 

77230 

77027 

76829 

76636 

76446 

76261 

.42 

76081 

75905 

75733 

75565 

75402 

75243 

75089 

74939 

74793 

74652 

•43 

7451S 

74382 

74254 

74130 

74010 

73894 

73783 

73676 

93574 

73746 

1.44 

73382 

73292 

73207 

73^5 

73°49 

72976 

72908 

72844 

72784 

72728 

*  Quoted  from  Carr's  "  Synopsis  of  Mathematics,"  and  is  there  quoted  from  Legendre's  "  Exercises  de  Calcul 
Integral,"  tome  ii. 

SMITHSONIAN  TABLES. 

38 


GAMMA   FUNCTION. 


TABLE  53, 


n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1.45 

9.9472677 

72630 

72587 

72549 

725U 

72484 

72459 

72437 

72419 

72406 

1.46 

72397 

72393 

72392 

72396 

72404 

72416 

72432 

72452 

72477 

72506 

1.47 

72539 

72576 

72617 

72662 

72712 

72766 

72824 

72886 

72952 

73022 

1.48 

73097 

73175 

73258 

73345 

73436 

73531 

7363° 

73734 

73841 

73953 

1.49 

74068 

74188 

74312 

74440 

74572 

74708 

74848 

74992 

75'4i 

75293 

1.50 

9-9475449 

75610 

75774 

75943 

76116 

76292 

76473 

76658 

76847 

77040 

I  rj 

77237 

77438 

77642 

77851 

78064 

78281 

78502 

78727 

78956 

79189 

1.52 

79426 

79667 

79912 

80161 

80414 

80671 

80932 

81196 

81465 

8173- 

T-53 

82015 

82295 

82580 

82868 

83161 

83457 

83758 

84062 

84370 

84682 

i-54 

84998 

85318 

85642 

85970 

86302 

86638 

86977 

87321 

87668 

88019 

1.55 

9.9488374 

88733 

89096 

89463 

89834 

90208 

90587 

90969 

91355 

91745 

1.56 

92139 

92537 

92938 

93344 

93753 

94166 

94583 

95004 

95429 

95857 

96289 

96725 

97165 

97609 

98056 

98508 

98963 

99422 

99885 

00351 

1-58 

500822 

01296 

01774 

02255 

02741 

03230 

03723 

04220 

04720 

05225 

05733 

06245 

06760 

07280 

07803 

08330 

08860 

09395 

09933 

1.60 

9.91:11020 

11569 

I2I22 

12679 

13240 

13804 

M372 

H943 

15519 

16098 

K6l 

16680 

17267 

17857 

18451 

19048 

19650 

20254 

20862 

21475 

22091 

1.62 

22710 

23333 

23960 

24591 

25225 

25863 

26504 

27149 

27798 

28451 

1.63 
1.64 

29107 
35867 

29767 
36563 

30430 
37263 

31097 
37966 

31767 
38673 

32442 
39383 

33120 
40097 

40815 

34486 
41536 

35175 
42260 

165 

9.9542989 

43721 

44456 

45195 

45938 

46684 

47434 

48187 

48944 

49704 

1.66 
1.67 

50468 
58303 

51236 
59106 

52007 
59913 

52782 
60723 

61536 

54342 
62353 

55^7 
63174 

55916 
63998 

56708 
64826 

57504 
65656 

1.68 

66491 

67329 

68170 

69015 

69864 

70716 

7T57J 

7243° 

73293 

Z4159, 

1.69 

75028 

76777 

77657 

78540 

79427 

80317 

81211 

82108 

83008 

1.70 

9-9583912 

84820 

85731 

86645 

87536 

88484 

89409 

90337 

91268 

22203 

1.71 

1.72 

602712 

94083 
03688 

95028 
04667 

95977 

96929 
06636 

97884 
07625 

98843 
08618 

99805 
09614 

00771 
10613 

01740 

11616 

1.74 

12622 
22869 

13632 
23912 

14645 
24959 

1566? 
26009 

16681 
27062 

17704 
28118 

18730 
29178 

19760 
30241 

20793 
31308 

21830 

32377 

1.75 

9-9633451 

34527 

35607 

36690 

37776 

38866 

39959 

41055 

42155 

43258 

1.76 

1.77 

1.79 

44364 

67176 
79070 

45473 
56749 
68351 
80277 

46586 

57894 
69529 
81488 

47702 

59043 
70710 
82701 

48821 
60195 
71895 
83198 

49944 
6135° 
73082 
85138 

51070 
62509 

74274 
86361 

52200 
63671 
75468 
87588 

53331 
64836 
76665 
88818 

C4467 
66004 
77866 
90051 

1.80 

1.81 

9.9691287 

703823 

92526 
05095 

93768 
06369 

95014 
07646 

96263 

08927 

975T5 

IO2II 

98770 
11498 

00029 
12788 

01291 
14082 

02555 
15378 

1.82 
1.83 

16678 
29848 

17981 
31182 

19287 

32520 

20596 
33860 

21908 

23224 
36551 

24542 
37900 

25864 
39254 

27189 
40610 

28517 
41969 

1.84 

43331 

44697 

46065 

47437 

48812 

50190 

5J57i 

52955 

54342 

55733 

1.85 

1.86 
1.87 

9.9757126 
71230 
85640 

58522 
72657 
87098 

59922 
74087 
88559 

61325 

75521 
90023 

62730 

76957 
91490 

64140 

78397 
92960 

79839 
94433 

66966 
81285 
9^910 

68384 
82734 
97389 

69805 
84186 

^s71 

1.88 
1.89 

800356 

*5374 

01844 
16893 

03335 
18414 

04830 
19939 

06327 
21466 

07827 
22996 

09331 
2453° 

10837 
26066 

12346 
27606 

29148 

1.90 

1.91 
1.92 

1.94 

9.9830693 
46311 
62226 
78436 
9493s 

32242 
47890 
63834 
80073 
96605 

33793 
4947  i 
65445 
81713 
98274 

35348 

5I055 
67058 

83356 
99946 

36905 
52642 

68675 
85002 
01621 

38465 
54232 
70294 
86651 
03299 

40028 

55825 
71917 
88302 
04980 

41595 

57421 

73542 

43l64 
59020 
75170 
91614 
08350 

44736 
60622 
76802 

10039 

1.95 

1.96 
1.97 
1.98 
1.99 

9.9911732 

28815 
46185 
63840 
81779 

13427 
30539 
47937 
65621 
83588 

49693 
67405 
85401 

16826 
33995 
5H51 
69192 
87216 

18530 

35728 

532J3 
70982 

89034 

20237 
37464 

54977 
72774 
90854 

21947 
39202 

56744 
74570 
92678 

23659 
40943 

756368 
94504 

25375 

60286 
78169 
96333 

27093 

44435 
62062 

79972 
98165 

SMITHSONIAN  TABLES. 


39 


TABLE  54. 

ZONAL   HARMONICS.* 

The  values  of  the  first  seven  zonal  harmonics  are  here  given  for  every  degree  between  9  ==  o°  and  6  =  90°. 


e 

* 

z, 

Z3 

Z4 

25 

zc 

Z7 

0° 

I.OOCO 

I.OOOO 

I.OOOO 

i  .0000 

I.OOOO 

1  .0000 

I.OOOO 

1° 

2 

3 

0.9998 

09995 
.9982 

•9959 

0.9991 

•9963 
.9918 

0.9985 

•9939 
.9863 

0.9977 
.9909 

•9795 

09967 
.9872 

0-9955 
.9829 
.9617 

4 

.9976 

.9927 

.9854 

•9758 

.9638 

•9495 

•9329 

5 

.9962 

.9886 

•9773 

.9623 

•9437 

.9216 

.8961 

6° 

•9945 
•9925 
•99°3 

.9836 

•9777 
.9709 

.9674 
•9557 
•9423 

•9459 

.9267 
.9048 

.9194 
.8911 
•8589 

.8881 

.8476 
•8053 

.8522 
.7986 
.7448 

9 

.9877 

•9633 

•9273 

.8803 

.8232 

•7571 

.6831 

10 

.9848 

•9548 

.9106 

•8532 

.7840 

•7045 

.6164 

11° 

.9816 

•9454 

.8923 

.8238 

•7417 

.6483 

.5461 

12 

.9781 

•9352 

.8724 

.7920 

.6966 

.5892 

•4732 

13 

•9744 

.9241 

.8511 

•7582 

.6489 

•5273 

•3940 

14 

•9703 

.9122 

.8283 

•599° 

•4635 

.  -3219 

15 

•9659 

•8995 

.8042 

'.6847 

•5471 

.3982 

•2454 

16° 

.9613 

.8860 

.7787 

.6454 

•4937 

•3322 

.1699 

17 

•9563 

.8718 

•75*9 

.6046 

•4391 

.2660     .0961 

18 

•9511 

.8568 

.7240 

•5624 

•3836 

.2002     .0289 

19 

•9455 

.8410 

•6950 

.5192 

•3276 

.1347  i  —.0443 

20 

-9397 

•8245 

.6649 

•475° 

•2715 

.0719 

—.1072 

21° 

•9336 

.8074 

•6338 

.4300 

.2156 

.0107 

—.1662 

22 

.9272 

•7895 

.6019 

.3845 

.1602 

—.0481 

—.2201 

23 

.9205 

.7710 

.5692 

•33^6 

•1057 

—.1038 

—.2681 

24 

•9!35 

•75J8 

•5357 

.2926 

•0525 

—  -J559 

—  -3°95 

25 

.9063 

.7321 

.5016 

.2465 

.0009 

—•2053 

-•3463 

26° 

.8988 

.7117 

.4670 

.2007 

—.0489 

-.2478 

—•3717 

27 

.8910 

.6908. 

•43  T  9 

•1553 

—.0964 

—.2869 

—.3921 

28 

.8829 

.6694 

•3964 

.1  105 

—•1415 

—.3211 

—.4052 

29 

.8746 

.6474 

.3607 

.0665 

-.1839 

—  -3SQ3 

—.4114 

30 

.8660 

.6250 

.3248 

.0234 

—•2233 

—•3740 

—.4101 

31° 

.8572 

.6021 

.2887 

—.0185 

—•2595 

—•3924 

—  .4022 

32 

.8480 

.5788 

.2527 

—.0591 

—  .2923 

—.4052 

-.38-6 

33 

.8387 

•5551 

.2.67 

—  .0982 

—.3216 

—  .4126 

—.3670 

34 

.8290 

•53jo 

.1809 

—•1357 

—•3473 

—.4148 

—•3409 

35 

.8192 

•H54 

—.1714 

—.3691 

—.4115 

—.3096 

36° 

.8090 

.4818 

.1102 

—.2052 

—3871 

—.4031 

—  2738 

37 

.7986 

•4567 

•0755 

—.2370 

—  .4011 

—.3898 

—  -2343 

38 

.7880 

•43*4 

.0413 

—.2666 

—.4112 

—•3719 

—  .1918 

39 

•7771 

•4059 

.0077 

—.2940 

—  .4174 

—•3497 

—.1469 

40 

.7660 

.3802 

—.0252 

—.3190 

—.4197 

—•3234 

—.1003 

41° 

•7547 

•3544 

—•0574 

—.3416 

-.4181 

—.2938 

—•0534 

42 

•7431 

.3284 

—.0887 

—.3616 

—.4128 

—.2611 

—  .0065 

43 

•73H 

•3023 

—  .1191 

—  -3791 

—.4038 

—.2255 

•°395 

44 

.2762 

—.1485 

—•3940 

—-39M 

—.1878 

.0846 

45 

.7071 

.2500 

—.1768 

—  .4062 

—•3757 

—.1485 

.1270 

*  Calculated  by  Prof.  Perry  (Phil.  Mag.  Dec.  1891).     See  also  A.  Gray,  "Absolute  Measurements  in  Electricity 
and  Magnetism,"  vol.  ii.,  part  2. 

SMITHSONIAN  TABLES. 

40 


ZONAL    HARMONICS. 


TABLE  54, 


e 

Zl 

Z2 

Z3 

Z4 

Z5 

Z6 

Z7 

46° 

0.6947 

0.2238 

—  .2040 

—.4158 

-.3568 

—.1079 

0.1666 

47 

.6820 

.1977 

—.2300 

—.4252 

—•335° 

—.0645 

•2054 

48 
49 

.6691 
.6561 

.1716 
.1456 

-l^Si 

—.4270 
—.4286 

—12836 

—  .0251 
.0161 

•2349 
.2627 

5° 

.6428 

.1198 

—.3002 

—•4275 

—•2545 

•0563 

.2854 

51° 

.6293 

.0941 

—.3209 

—•4239 

—•2235 

•0954 

•3031 

52 

.0686 

—.3401 

—.4178 

—  .1910 

.1326 

•3i53 

53 

]6oi8 

•0433 

—3578 

—•4093 

—•I57I 

.1677 

.3221 

54 

.5878 

.0182 

—•3740 

-.3984 

—  .1223 

.2002 

•3234 

55 

•5736 

—  .0065 

-.3886 

-•3852 

—.0868 

.2297 

56° 

•5592 

—  .0310 

—  .4016 

-.3698 

—  .0510 

•2559 

•3095 

57 

•5446 

—•0551 

—-4I31 

—•3524 

—  .0150 

•2787 

.2949 

58 

•5299 

—.0788 

—.4229 

—  -333  T 

.0206 

.2976 

•2752 

59 

•5*50 

—  .1021 

—•43  T° 

—  -31  19 

•°557 

•3125 

.2511 

60 

.5000 

—.1250 

—•4375 

—.2891 

.0898 

•3232 

.2231 

61° 

.4848 

—.1474 

—•4423 

—2647 

.1229 

.3298 

.1916 

62 

.4695 

—.1694 

—•4455 

—.2390 

•1545 

.3321 

•1571 

63 

•4540 

—.1908 

—.4471 

.  2  1  2  1 

.1844 

•3302 

.1203 

64 

•4384 

—.2117 

—  4470 

—.1841 

.2123 

.3240 

.0818 

65 

.4226 

—.2321 

—•4452 

—  -T552 

.2381 

•3138 

.0422 

66° 

.4067 

-.2518 

—.4419 

-.1256 

.2615 

.2996 

.0021 

67 
68 

•3907 
•3746 

—  .2710 
-.2896 

—•43/0 
—•4305 

—•°955 
—  .0650 

.2824 
•3005 

.2819 
.2605 

—•0375 
—.0763 

69 

•3584 

—  -3°74 

—.4225 

—•0344 

•3158 

.2361 

—  -"35 

70 

.3420 

—•3425 

—.4130 

—.0038 

.3281 

.2089 

—.1485 

71° 

•3256 

—.3410 

—  .4021 

.0267 

•3373 

.1786 

—.1811 

72 
73 

.3090 
.2924 

-.3568 

-.3898 
—.3761 

.0568 
.0864 

•3434 
•3463 

.1472 
.1144 

—.2099 
—.2347 

74 

.2756 

—.'3860 

—  .3611 

•"53 

.3461 

•0795 

—•2559 

75 

.2588 

—•3995 

—•3449 

•1434 

•3427 

.0431 

—.2730 

76° 

77 
78 
79 
80 

.2419 
.2250 
.2079 
.1908 
•1736 

—  .4112 
—.4241 
—•4352 
—•4454 
-4548 

—•3275 
—.3090 

—.2474 

•1705 
.1964 

.221  I 

•2443 
.2659 

.3362 
•3267 
•3M3 
.2990 
.2810 

.0076 
—.0284 
—.0644 
-.0989 
—.1321 

—.2848 
—.2919 

—•2943 
-.2913 

—2835 

81° 

82 

.1564 
.1392 

-4633 
—  .4709 

—2251 
—  .2020 

.2859 
.3040 

.2606 

.2378 

-1635 
—  .1926 

-.2709 
—•2536 

83 
84 

85 

.1219 

.1045 
.0872 

—•4777 
—.4836 
-.4886 

—  1783 
—•'539 
—  .1291 

•3203 
•3345 
.3468 

.2129 
.1861 

•1577 

—.2193 

—  -2431 
—.2638 

—.2321 
—  .2067 
—.1779 

86° 

1 

89 

.0698 
.0523 
•0349 
•OI75 

—.4927 

—•4959 
-.4982 

—•4995 

—.1038 
—.0781 
—  .0522 
—  .0262 

•3704 
•3739 

.1278 
.0969 
.0651 
.0327 

—.2811 
—.2947 
—•3045 
—  -3I05 

—  .1460 
—.1117 

—0735 

90 

.0000 

—  .5000 

—.0000 

•3750 

.0000 

—  -3T25 

—  .0000 

SMITHSONIAN  TABLES. 


TABLE  55. 


MUTUAL  INDUCTANCE, 


Values  of  log 


M 


Table  of  values  of  log  —  . for  facilitating  the  calculation  of  the  mutual  inductance  M  of  two  coaxial  circles  of 

4 irVaa'  t  fa — ai 

radii  a,  a',  £\  distance  apart  6.     The  table  is  calculated  for  intervals  of  6/  in  the  value  of  cos-1  \ 

from  60°  to  90°. 


0' 

6' 

12' 

18' 

24 

30' 

36' 

42' 

48' 

54' 

60° 

1.4994783 

5022651 

5050505 

5078345 

5106173 

5133989 

5161791 

5189582 

5217361 

5245128 

61 

5272883 

5300628 

5328361 

5356084 

5383796 

5411498 

5439  i  90 

5466872 

5494545 

5522209 

62 

5549864 

5577510 

5605147 

5632776 

5660398 

5688011 

5715618 

5743217 

5770809 

5798394 

63 

5825973 

5853546 

5881113 

5908675 

5936231 

5963782 

5991322 

6018871 

6046408 

6073942 

64 

6101472 

6128998 

6156522 

6184042 

6211560 

6239076 

6266589 

6294101 

6321612 

6349121 

65° 

66 

1.6376629 
6651732 

6404137 
6679250 

643*645 

6706772 

6459153 
6734296 

6486660 
6761824 

6514169 
6789356 

6541678 
6816891 

6569189 
6844431 

6596701 
6871976 

6624215 
6899526 

67 

6927081 

6954642 

6982209 

7009782 

7037362 

7064949 

7092544 

7120146 

7M7756 

7175375 

68 

7203003 

7230640 

7258286 

7285942 

7313609 

7341287 

7368975 

7396675 

7424387 

7452111 

69 

7479848 

7507597 

753536i 

7563138 

7590929 

7618735 

7646556 

7674392 

7702245 

7730114 

70° 

1.7758000 

7785903 

7813823 

7841762 

7869720 

7897696 

7925692 

7953709 

798i745 

8009803 

7i 

8037882 

8065983 

8094107 

8122253 

8150423 

8178617 

8206836 

823508018263349 

8291645 

72 

8319967 

8348316 

8376693 

8405099 

8433534 

8461998 

8490493 

8519018 

8547575 

8576164 

73 

8604785 

8633440 

8662129 

8690852 

8719611 

8748406 

8777237 

8806106 

8835013 

8863958 

74 

8892943 

8921969 

8951036 

8980144 

9009295 

9038489 

9067728 

9097012 

9126341 

9I557I7 

75° 

1.9185141 

9214613 

9244135 

9273707 

9303330 

9333005 

9362733 

939*5'  5 

9422352 

9452246 

76 

9482196 

9512205 

9542272 

9572400 

9602590 

9632841 

9663157 

9693537 

9723983 

9754497 

77 

9785079 

98i573i 

9846454 

9877249 

9908118 

9939062 

9970082 

ooonST 

0032359 

0063618 

78 

0.0094959 

0126385 

0157896 

0189494 

0221181 

0252959 

0284830 

0316794 

0348855 

0381014 

79 

O4r3273 

04456.33 

0478098 

0510668 

0543347 

0576136 

0609037 

0642054 

0675187 

0708441 

80° 

0.0741816 

0775316 

0808944 

0842702 

0876592 

0910619 

0944784 

0979091 

1013542 

1048142 

81 

1082893 

1117799 

1152863 

1188089 

1223481 

1259043 

1294778 

1330691 

1366786 

1403067 

82 

M39539 

1476207 

i5I3°75 

i  55°  r  49 

i  587434 

1624935 

1662658 

i  700609 

1738794 

1777219 

83 

1815890 

1854815 

1894001 

1933455 

1973184 

2013197 

2053502 

2094108 

2135026 

2176259 

84 

2217823 

2259728 

2301983 

2344600 

2387591 

2430970 

2474748 

2518940 

2563561 

2608626 

85° 

0.2654152 

2700156 

2746655 

2793670 

2841221 

2889329 

2938018 

2987312 

3037238 

3087823 

86 

3  J  39097 

3191092 

3243843 

3297387 

3351762 

3407012 

3463184 

3520327 

3578495 

3637749 

87 

3698153 

3759777 

3822700 

3887006 

3952792 

4020162 

4089234 

4160138 

4233022 

4308053 

88 

4385420 

4465341 

4548064 

4633880 

4723127 

4816206 

49r3595 

5015870 

5I23738 

5238079 

89 

5360007 

5490969 

5632886 

5788406 

5961320 

6157370 

6385907 

6663883 

7027765 

7586941 

*  Quoted  from  Gray's  "  Absolute  Measurements  in  Electricity  and  Magnetism,"  vol.  ii.,  p.  852. 
SMITHSONIAN  TABLES. 


ELLIPTIC   INTEGRALS. 


Values  of 


pa- 
Jo 


sin2  e  sin2  < 


This  table  gives  the  values  of  the  integrals  between  o  and  n / 2  of  the  function  (i — sin20sin2<£) 
ues  of  the  modulus  corresponding  to  each  degree  of  6  between  o  and  90. 


TABLE  56. 


for  different  val- 


6 

fl     «* 

f*I 
0 

6   ' 

n 

* 

r* 

L/O 

/O   (i—  sin20sin2<J»)* 

JQ  (i—  sin20sin2<£)* 

lumber. 

Log. 

lumber. 

Log. 

Number. 

Log. 

Dumber. 

Log. 

0° 

.5708 

0.196120 

.5708 

0.196120 

45° 

.8541 

0.268127 

•35°6 

.130541 

I 

5709 

I96I53 

5707 

196087 

6 

8691 

271644 

3418 

127690 

2 

5713 

196252 

5703 

195988 

7 

8848 

275267 

3329 

124788 

3 

5719 

196418 

5697 

195822 

8 

9011 

279001 

3^8 

121836 

4 

5727 

196649 

5689 

'9559* 

9 

9180 

282848 

3'47 

118836 

5° 

.5738 

0.196947 

.5678 

0.195293 

50° 

1.9356 

0.2868II 

•3055 

0.115/90 

6 

5751 

197312 

5665 

194930 

i 

9539 

290895 

112698 

7 

5767 

197743 

5649 

194500 

2 

9729 

295101 

2870 

109563 

8 

5785 

197241 

5632 

194004 

3 

9927 

299435 

2776 

106386 

9 

5805 

198806 

5611 

193442 

4 

2.0133 

268l 

103169 

10° 

1.5828 

0.199438 

1.5589 

0.192815 

55° 

2.0347 

0.308504 

.2587 

0.099915 

i 

5854 

200137 

5564 

192121 

6 

0571 

313247 

2492 

096626 

'  2 

5882 

200904 

5537 

191302 

7 

0804 

318138 

2397 

093303 

3 

59*3 

201740 

55°7 

190537 

8 

1047 

323182 

2301 

089950 

4 

5946 

202643 

5476 

189646 

9 

1300 

328384 

22O6 

086569 

15° 

6 

1.5981 

6020 

0.203615 

204657 

1.5442 
5405 

0.188690 
187668 

60° 

i 

2.1565 
1842 

0.333753 
339295 

I.2III 

2015 

0.083164 
079738 

7 

6061 

205768 

5367 

186581 

2 

2132 

345020 

I92O 

076293 

8 

6105 

206948 

5326 

185428 

3 

2435 

350936 

1826 

072834 

9 

6151 

208200 

5283 

184210 

4 

2754 

357053 

1732 

069364 

20° 

1.6200 

0.209522 

1.5238 

0.182928 

65° 

2.3088 

0.363384 

1.1638 

0.065889 

i 

6252 

210916 

5191 

181580 

6 

3439 

369940 

1545 

062412 

2 

6307 

212382 

180168 

7 

3809 

376736 

1453 

058937 

3 

6365 

213921 

5090 

178691 

8 

4198 

383787 

1362 

055472 

4 

6426 

215533 

5037 

177150 

9 

4610 

39III2 

1272 

052020 

25° 

6 

7 

1.6490 

6557 
6627 

0.217219 

218981 
220818 

1.4981 
4924 
4864 

0.175545 
173876 

172144 

70° 

i 

2 

2.5046 
5507 
5998 

0.398730 
406665 
4M943 

I.II84 
1096 

ion 

0.048589 
045183 
04l8l2 

8 
9 

6701 
6777 

222732 
224723 

4803 
4740 

170348 
168489 

3 
4 

6521 
7081 

423596 
432660 

0927 
0844 

038481 
035200 

30° 

i 

2 

3 
4 

1.6858 
6941 
7028 
7119 
7214 

0.226793 

228943 
23H73 
233485 
235880 

1.4675 
4608 

4539 
4469 
^397 

0.166567 
164583 
162537 
160429 
158261 

75° 

6 

9 

2.7681 

8327 
9026 
9786 
3.0617 

0.442176 
452196 
462782 
474008 
485967 

1.0764 
0686 
0611 
0538 
0468 

0.031976 
028819 
025740 
022749 
019858 

35° 

6 

9 

1.7312 

7522 

7633 
774» 

0.238359 
240923 
243575 
246315 
249146 

1.4323 
4248 
4171 
4092 
4013 

0.156031 
153742 
15*393 
148985 
146519 

80° 

2 

3 
4 

2553 
3699 
5004 

6519 

0.498777 
512591 
527613 
544120 
562514 

1.0401 
0338 
0278 
0223 
0172 

O.OI708I 
014432 
OII927 
009584 
007422 

40° 

2 

3 
4 

1.7868 
7992 
8122 
8256 
8396 

0.252068 
255085 
258197 
261406 
264716 

i-393r 
3849 
3765 
3680 

3594 

0.143995 
141414 
138778 
136086 
133340 

85° 

6 

i 

9 

3.8317 
4.0528 

3387 
7427 
5-4349 

0.583396 
607751 

637355 
676027 

735192 

1.0127 
0086 
0053 
0026 
0008 

0.005465 
003740 
002278 
OOII2I 
000326 

45° 

1.8541 

0.268127 

1-3506 

0.13054! 

90° 

oo 

oo 

I.OOOO 

SMITHSONIAN  TABLES. 


43 


TABLE  57. 


BRITISH   UNITS. 

Gross  sections  and  weights  of  wires. 


This  table  gives  the  cross  section  and  weights  in  British  units  of  copper,  iron,  and  brass  wires  of  the  diameters 
given  in  the  first  column.  For  one  tenth  the  diameter  divide  section  and  weights  by  100.  For  ten  times  the 
diameter  multiply  by  100,  and  so  on. 


c 

1-2 

la 

Q 

Area  of 
cross 
section 
in 
Sq.  Mils. 

Copper  —  Density  8.  go. 

Iron  —  Density  7.80. 

Brass  —  Density  8.56. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

10 

78.54 

.000303 

4.48150 

33°0- 

.0002656 

4.42420 

3765. 

.0002915 

4.46458 

3431- 

n 

95-°3 

0367 

.56429 

2727. 

03214 

.50697 

3II2. 

03527 

54735 

2836. 

12 

113.10 

0436 

.63986 

2291. 

03825 

.58257 

2615. 

04197 

62295 

2383. 

!3 

132-73 

0512 

•70939 

J953- 

04488 

.65208 

2228. 

04926 

69246 

2030. 

14 

153-94 

0594 

•77376 

1683. 

05206 

.71646 

1921. 

05713 

75684 

17S°- 

15 

176.71 

.000682 

4.83368 

1467. 

.0005976 

4-77637 

1674, 

.0006558 

4.81675 

1525- 

16 

201.06 

0776 

.88974 

1289. 

06799 

.83244 

1471. 

07461 

.87282 

1340. 

17 

226.98 

0876 

.94240 

1142. 

07675 

.88510 

!303- 

08423 

.92548 

1187. 

18 

25447 

0982 

•99205 

1018. 

08605 

•93475 

1162. 

09443 

•97513 

1059. 

J9 

283-53 

1094 

3.03902 

914. 

09588 

.98171 

1043. 

.0010522 

3.02209 

95°- 

20 

314.16 

.OOI  21  2 

3-08357 

825.1 

.001062 

3.02626 

941.4 

.001166 

3.06664 

857-7 

21 

346-36 

T336 

.12594 

748.3 

1171 

.06864 

853-8 

1285 

.10902 

778.0 

22 

380.13 

1467 

.16634 

681.8 

1286 

.10904 

777-8 

1411 

•14942 

708.9 

23 

415.48 

1603 

.20496 

623.8 

1405 

.14766 

711.7 

1542 

.18804 

648.6 

24 

452.39 

1746 

.24192 

572-9 

1530 

.18463 

653-7 

1679 

.22500 

595-7 

25 

490.87 

.001894 

3-27738 

528.0 

.OOl66o 

3.22008 

602.4 

.001822 

3.26046 

549-0 

26 

53P-93 

2046 

.31146 

488.1 

*795 

•25415 

557-o 

1970 

•29453 

507-5 

27 

572-56 

2209 

•34423 

452.6 

1936 

•28693 

5*6.5 

2I25 

•3273< 

470.6 

28 

6i5-75 

2376 

•37583 

420.9 

2082 

.31852 

480.3 

2285 

•35890 

437-6 

29 

660.52 

2549 

.40630 

392.4 

2234 

.34900 

447-7 

2451 

•38938 

408.0 

30 

706.82 

.002727 

3-43575 

366.7 

.002390 

3-37845 

418.4 

.002623 

3.41882 

381.2 

3^ 

754-77 

2912 

.46424 

343-4 

2552 

•40693 

391.8 

2801 

•44731 

357-o 

32 

804.25 

3I03 

.49181 

322.2 

2720 

•43450 

367-7 

2985 

.47488 

335-i 

33 
34 

855-30 
907.92 

33oo 
35°3 

•51854 
.54446 

303-0 
285.4 

2892 
3070 

.46123 
.48716 

345-8 

325-7 

3^74 
3369 

.50161 

•52754 

3I5-1 
296.8 

35 

962.11 

.003712 

3-56964 

269.4 

•003253 

%J*J  ^-JO 

3°7-4 

.003570 

3-5527I 

280.1 

36 

1017.88 

4927 

.59412 

254.6 

3442 

.5360! 

290.5 

3777 

•57719 

264.7 

37 

1075.21 

4149 

.61791 

241.0 

3636 

.56061 

275.0 

3990 

.60098 

250.6 

38 

1134.11 

4376 

.64108 

228.5 

3844 

.58476 

260.2 

4218 

.62514 

237-1 

39 

1194.59 

4609 

.66364 

216.9 

4040 

•60633 

247.6 

4433 

.6467  1 

225.6 

40 

1256.64 

.004849 

3.68563 

206.2 

.004249 

3-62833 

235-3 

.004664 

3.66871 

214.4 

4i 

1320.25 

5°94 

.70708 

196.3 

4465 

.64977 

224.0 

4900 

.69015 

204.1 

42 

1385.44 

5346 

.72801 

187.1 

4685 

.67070 

213-5 

5r4i 

.71108 

J94-5 

43 

1452.20 

5603 

•74845 

178-5 

4911 

.69114 

203.6 

5389 

•73152 

185.6 

44 

1  520.53 

5867 

.76842 

170.4 

5J42 

.71111 

194-5 

5643 

•75*49 

177.2 

45 

1590.43 

.006137 

3-78793 

162.9 

•005378 

3-73063 

185.9 

.005902 

3.77101 

169.4 

46 

1661.90 

6412 

.80703 

J55-9 

5620 

.74972 

177.9 

6167 

.79010 

162.1 

47 

1734-94 

6694 

.82569 

•149.4 

5867 

.76840 

170.5 

6438 

.80878 

T55-3 

48 

1809.56 

6982 

.84399 

143.2 

6119 

.78669 

163.4 

6715 

.82706 

148.9 

49 

1885.74 

7276 

.86289 

137-4 

6377 

.80459 

156.8 

6998 

.84497 

142.9 

50 

51 

1963.50 

2042.82 

.007576 
7882 

3-87945 
.89664 

132.0 
126.9 

.006640 
6908 

3.82214 
•83934 

150.6 
144.8 

.007287 
758r 

3.86252 
.87972 

137-2 
I3I-9 

52 

2123.72 

8194 

•9i352 

I22.O 

7181 

.85621 

139.2 

7881 

.89659 

126.9 

53 

2206.18 

8512 

•93005 

II7-5 

7460 

•87275 

134.0 

8187 

W31  3 

122.  1 

54 

2290.22 

8837 

.94630 

II3.2 

7744 

.88899 

129.1 

8499 

•92937 

1177 

55 

2375-83 

.009167 

3.96223 

109.1 

.008034 

3-90493 

124.5 

.008817 

3-94531 

"3-4 

SMITHSONIAN  TABLES. 


44 


TABLE  57, 


BRITISH   UNITS. 

Gross  sections  and  weights  of  wires. 


e 
"~-J2 

£  M 
if 

Area  of 
cross 
section 
in 
Sq.  Mils. 

Copper  —  Density  8.90. 

Iron  —  Density  7.80. 

Brass  —  Density  8.56. 

Pounds 
per  Foot. 

Log. 

?eet  per 
Pound. 

Pounds 
per  Foot. 

Log. 

Feet  per 
Pound. 

Pounds 
jer  Foot. 

Log. 

Feet  per 
Pound. 

55 

2375-83 

009167 

3.96223 

IO9.I 

.008034 

3-90493 

124.5 

.008817 

3-94531 

113-4 

56 

2463.01 

09504 

.97789 

105.2 

08329 

.92058 

1  2O.  I 

09140 

.96096 

109.4 

P 

2551.76 
2642.08 

09846 
10195 

•99325 
2.00837 

101.6 
98.1 

08629 
08934 

•93595 
.95106 

"5-9 
111.9 

09470 
09805 

•97633 
_-99l44 

105.6 
102.0 

59 

2733-97 

10549 

.02320 

94-8 

09245 

.96591 

108.2 

10146 

2.00629 

98.6 

60 

2827.43 

01091 

2.03782 

91.66 

.00956 

3.98050 

104.59 

.01049 

2.02088 

95-3° 

61 

2922.47 

1128 

.05216 

88.68 

0988 

.99486 

101.19 

1085 

•03524 

92.21 

62 

3019.07 

1165 

.06628 

85.84 

IO2I 

2.00898 

97-95 

1  1  2O 

89.25 

63 

3IJ7-25 

1203 

.08019 

83.14 

1054 

.02288 

94.87 

"57 

.06326 

86.45 

64 

3216.99 

1241 

.09386 

80.56 

1088 

.03656 

91.83 

1194 

.07694 

8377 

65 

33l8-3T 

01280 

2.10732 

78.11 

.OII22 

2.05003 

89.12 

.01231 

2.09041 

81.21 

66 

3421.19 

1320 

.12061 

75-76 

H57 

.06329 

86.44 

1270 

.10367 

78.76 

67 

3525-65 

1360 

•13367 

73-51 

1192 

•07635 

83.88 

1308 

.11673 

76.43  1 

68 

3631.68 

I4OI 

•14655 

71-36 

1228 

.08922 

81.42 

1348 

.12960 

74.20 

69 

3739-28 

1443 

.15924 

69.3° 

1264 

.10190 

79-09 

1388 

.14228 

72.06 

70 

71 

384845 
3959-J9 

.01485 
1528 

2.17174 
.18404 

67-34 
65.46 

.01302 

J339 

2.11451 
.12672 

76.82 
74.69 

.01429 
1469 

2.15489 
.16710 

70.00 

68.06 

72 

4071.50 

1571 

.19618 

63.65 

1377 

.13887 

72.63 

IS" 

•17925 

66.19 

73 
74 

4185-39 
4300.84 

1615 
1660 

.20817 
.22OOO 

61.92 
60.26 

1415 
1454 

•T^5 
.16267 

70.66 
68.76 

!553 
1596 

.19123 
.20304 

64.38 

75 

4417.86 

.01705 

2.23165 

58.66 

.01494 

2.17432 

66.95 

.01639 

2~.  2  1  460 

61.01 

76 

£ 

4536.46 
4656.63 
4778.36 

I751 
1797 
1844 

•24317 
•25453 
.26574 

57-13 
55-65 
54-23 

1534 
J575 
1616 

.18583 
.19718 
•20839 

65.19 

63-5° 
61.89 

1684 
1728 
1773 

.22621 

.23756 

.24877 

59-40 
57-87 
56.39 

79 

4901.67 

1892 

.27681 

52-87 

1658 

.21946 

60.33 

1819 

•25974 

54-99 

80 

5026.55 

.01939 

2.28769 

5i-56 

.01700 

2.23038 

58.83 

.01865 

2.27076 

53-6i 

81 

5153.00 

1988 

.29848 

50.29 

1743 

.24117 

57-39 

1912 

•28155 

52.29 

82 

83 
84 

5281.02 
5410.61 

5541-77 

2038 
2088 
2138 

.30914 
.31966 
.33006 

49.07 
47.90 
46.77 

1786 
1830 
1874 

.25183 
.26236 
.27276 

56.00 
54.66 
53-36 

1960 
2008 
2057 

.29221 
.30274 

•a'SH 

51-03 
49.80 

48-63 

85 

86 

5674-50 

5808.80 

.02189 
2241 

2.34034 

•35°5° 

45-67 
44.62 

.01919 
1964 

2.28304 
.29320 

52.11 
50.91 

.02106 
2156 

2.32342 
•33358 

47-49 
46.39 

87 

5944.68 

2294 

•36054 

43.60 

2010 

•30324 

49-75 

2206 

•34362 

45-33 

88 
89 

6221.14 

2347 
2400 

•37047 
.38028 

42.61 
41.66 

2057 
2IO4 

-3*317 
•32298 

48.62 
47-54 

2257 
2309 

•35355 
•36336 

44-3° 
43-31 

90 

91 

92 

93 
94 

6361.73 

6503.88 
6647.61 
6792.91 
6939.78 

•02455 
2509 

2565 
2621 
2678 

2.38999 

•39958 
.40908 
.41847 
•42775 

40.74 
39-85 
38.99 
38-15 
37-35 

.O2I5I 
2199 

2248 
2297 
2347 

2.33269 
•34228 
•35178 
.36116 
.37046 

46-49 
45-47 
44.49 

43-54 
42.61 

.02360 
2414 
2467 
2521 

2575 

2.37297 
.38266 
.39216 
.40154 
.41084 

42.37 
4i-43 
40-54 
39-67 
38-83 

95 

96 

97 
98 

99 

7088.22 

7238-23 
7389.81 
7542.96 
7697.69 

•02735 
2793 
2851 
2910 
2970 

2.43694 
.44604 
.45404 
•46395 
.47277 

36-56 
35-8i 
35-°7 
34-36 
33-67 

.02397 
2448 
2499 

2551 
2603 

2-37965 

.38874 

•39775 
.40665 

•41547 

41.72 
40.86 
40.02 

$Z 

.02630 
2686 
2742 
2799 
2857 

2.42003 
.42912 
.43812 
•44703 
.45585 

38.02 

37-37 
36.46 

35-72 
35-oi 

100 

7853-98 

.03030 

2.48150 

33-oo 

.02656 

2.42420 

37.65 

•02915 

2.46458 

34-31 

SMITHSONIAN   TABLES. 


45 


TABLE  58. 


METRIC  UNITS. 


Gross  sections  and  weights  of  wires. 

This  table  gives  the  cross  section  and  the  weight  in  metric  units  of  copper,  iron,  and  brass  wires  of  the  diameters 
given  in  the  first  column.  For  one  tenth  the  diameter  divide  sections  and  weights  by  100.  For  ten  times  the 
diameter  multiply  by  100,  and  so  on. 


Diam.  in  thou- 
sandths of  a  cm.  II 

Area  of  cross 
section. 

Copper  —  Density  8.90. 

Iron  —  Density  7.80. 

Brass  —  Density  8.56. 

itai 

Log. 

"qj    D    CC 

j|j 

Log. 

Metres 
per 
Gramme. 

fa 

Log. 

Jil 

<     O 

10 

78.54 

0.06990 

2.84448 

14.306 

0.06126 

2.78718 

16.324 

0.06723 

2.82756 

14.874 

II 

95-03 

.08458 

•92725 

11.823 

.07412 

.86996 

13.492 

•08135 

.91034 

12.293 

12 

113.10 

.10065 

1.00285 

9-935 

.08822 

•94556 

n-335 

.09681 

•98594 

10.330 

13 

132-73 

.iiSii 

•07236 

8.465 

•'0353 

1.01506 

9-659 

.11362 

1-05544 

8.801 

H 

153.94 

.13701 

•13674 

7.299 

.I200b 

•07945 

8.328 

•I3I77 

.11983 

7.589 

15 

176.71 

0-1573 

7.19665 

6.358 

0.1378 

^3936 

7-255 

0.1513 

7.17974 

6.6II 

1     16 

201.06 

.1789 

.25272 

5.588 

.1568 

.19542 

6.376 

.1721 

.23580 

5.810 

;    17 

226.98 

.2020 

•30538 

4-951 

.1770 

.24808 

5.648 

•T943 

.28846 

5-M7 

18 

254-47 

.2265 

•35503 

4-4I5 

.1985 

.29773 

5.038 

.2178 

.3381  r 

4-591 

19 

283-53 

•2523 

.40199 

.2212 

.34469 

4.522 

.2427 

•38507 

4.120 

20 

314.16 

0.2796 

7.44654 

3-577 

0.2450 

7.38925 

4.081 

0.2689 

7.42963 

3-7I9 

21 

346-36 

•3083 

.48892 

.244 

.2702 

.43162 

3-7oi 

.2965 

.47200 

•373 

22 

380.13 

•3383 

.52932 

2.956 

.2965 

.47203 

•373 

•3254 

.51241 

•073 

23 

4I5-48 

.3698 

.56794 

.704 

.3241 

.  5  1  064 

.086 

•3557 

.55^3 

2.812 

24 

452.39 

.4026 

.60490 

.484 

•3529 

.54;6i 

2.834 

•3872 

.58799 

.582 

25 

490.87 

0.4369 

7.64036 

2.289 

0.3829 

i.  58306 

2.612 

0.4202 

7.62344 

2.380 

26 

530-93 

•4725 

•67443 

.116 

.4141 

.61713 

-415 

•4545 

•65751 

.200 

27 

572.56 

.5096 

.70721 

1.962 

.4466 

.64992 

•239 

.4901 

.69030 

.040 

28 

6i5-75 

.5480 

.73880 

.825 

.4803 

.68150 

.082 

•5271 

.72188 

1.897 

29 

660.'  5  2 

•5879 

.76928 

.701 

.5'52 

.71198 

1.941 

.5654 

.75236 

.769 

30 

706.86 

754-77 

0.6291 
.6717 

7.79872 
.82721 

1.590 
.489 

055*4 

.5887 

.76991 

1.814 
.699 

0.6051 
.6461 

7.78181 
.81029 

"58 

32 

804.25 

.7158 

.85478 

•397 

.6273 

•79749 

•594 

.6884 

•83787 

•453 

33 

855-30 

.7612 

.88151 

•3*4 

.6671 

.82421 

•499 

•7321 

.86459 

•366 

34 

907.92 

.8081 

.90744 

.238 

.7082 

.85014 

.412 

7772 

.89052 

.287 

35 

962.  r  i 

0.856 

7.93261 

1.168 

0.7504 

1.87531 

1-333 

0.8236 

7.91570 

1.214 

36 

1017.88 

.906 

•95709 

.104 

•7939 

.89979 

.260 

•8713 

•94017 

.148 

H 

1075.21 
1134.11 

•957 

I.O12 

.98088 
0.00504 

•045 
0.988 

•83*7 
.8866 

•92359 
•94775 

.192 
.128 

.9204 
•973° 

.96397 
.98813 

.087 
.028 

39 

1194.59 

-063 

.02661 

.941 

.9318 

.96931 

•073 

1.0230 

0.00969 

0.978 

40 

1256.64 

Ml8 

0.04861 

0.8941 

0.980 

7.99131 

I.02OO 

1.076 

0.03169 

0.9296 

41 

1320.25 

••75 

.07005 

.8511 

1.030 

0.01275 

0-97II 

.130 

•°53  '3 

.8849 

42 

1385.44 

•233 

.09098 

.8110 

.081 

.03368 

•9254 

.186 

.07406 

•8432 

43 

1452.20 

.292 

.11142 

.7738 

•133 

.05412 

.8828 

•243 

•0945° 

.8044 

44 

1  520.  53 

•353 

•I3I39 

.7389 

.186 

.07409 

.8432 

.302 

.11447 

.7683 

45 

1590.43 

1.415 

0.15091 

0.7065 

1.241 

0.09361 

0.806  1 

1.361 

0.13399 

0-7345 

46 

1661.90 

•479 

.  1  7000 

.6761 

.296 

.11270 

"77H 

•423 

•15308 

.7029 

47 
48 
49 

734-94 
809.56 

885.74 

•544 
.611 
.678 

.18868 
.20696 
.22487 

.6476 
.6209 
•5958 

•353 
.411 

.471 

•13138 
.14967 
.16758 

•7389 
•7085 

•6799 

•485 
•549 
.614 

.17176 
.19005 
.20796 

•6734 
.6456 

•6195 

50 

51 

963-5° 
2042.82 

•748 
.818 

0.24242 
.25962 

0.5722 
•5500 

r-532 
•593 

0.18513 
.20232 

0.6530 
.6276 

1.681 

•753 

0.22551 
•24371 

0.5950 

•5705 

S2 

2123.72 

.890 

.27649 

.5291 

•657 

.21919 

.6037 

.818 

•25957 

•5501 

53 

2206.18 

•964 

.29303 

•5093 

.721 

•23574 

.5811 

.888 

.27612 

•5295 

54 

2290.22 

2.038 

.30927 

.4906 

.786 

•25197 

•5598 

.960 

•29235 

.5101 

55 

2375-83 

2.114 

0.32521 

0.4729 

•853 

0.26791 

0.5396 

2.034 

0.30829 

0.4917 

SMITHSONIAN  TABLES. 


46 


TABLE  58. 


METRIC  UNITS. 

Cross  sections  and  weights  of  wires. 


Diam.  in  thou- 
sandths of  a  cm.  1 

Area  of  cross 
section. 

Copper  —  Density  8.90. 

Iron  —  Density  7.80. 

Brass  —  Density  8.56. 

Ill 

Log. 

V 

*  ao 

Id 

Log. 

Metres 
per 
Gramme. 

1  fcg 

Log. 

Metres 
per 
Gramme. 

55 

2375-83 

2.114 

0.32521 

•4729 

1-853 

0.26791 

•5-396 

2-034 

0.30829 

.4917 

56 

2463.01 

.192 

.34086 

.4562 

.921 

.28356 

•5205 

.108 

•32394 

•4743 

59 

2551.76 
2642.08 
2733-97 

.271 
•351 

•433 

•35623 

•4403 

•4253 
4112 

.990 
2.061 
.132 

.29893 
.31404 
•32889 

.5024 
•4852 
.4689 

.184 
.262 

•340 

•3393  * 
•35442 

•4578 
.4422 

•4273 

60 

2827.43 

2.516 

0.40078 

•3974 

2.205 

0-34349 

•4534 

2.420 

0.38387 

.4132 

61 

2922.47 

.601 

•415*4 

•3845 

.280 

.35784 

•4387 

.502 

•39823 

•3997 

62 

3019.07 

.687 

.42926 

•3722 

•355 

•37196 

.4246 

•41235 

.3869 

63 

31  17.25 

•774 

.44316 

•3604 

•43  * 

•38587 

.4113 

.668 

.42625 

•3748 

64 

3216.99 

•863 

-45684 

•3493 

•509 

•39954 

•3985 

.760 

.44092 

•3623 

65 

3318.31 

2-953 

0.47031 

•3386 

2.588 

0.41301 

•3864 

2.840 

0-45339 

.3521 

66 

3421.19 

.48357 

•3284 

.669 

.42627 

•3747 

•929 

.46665 

•34*5 

67 

.138 

.49663 

•3187 

•75° 

•43933 

•3636 

3.018 

•47971 

•33*3 

68 

363I-68 

.232 

•50950 

•3°94 

.833 

.45220 

•353° 

.109 

.49258 

•3217 

.  69 

3739-28 

.328 

.52218 

•3005 

.917 

.46488 

•3429 

.201 

.50526 

•3*24 

70 

3848.45 

3.426 

0-53479 

.2919 

3-003 

0.47749 

•3330 

3.295 

0.51787 

•3035 

71 

3959-  *  9 

•524 

.54700 

.2838 

.088 

.48970 

•3238 

.389 

.53008 

.2951 

72 

4071.50 

.624 

•559*5 

•2759 

.176 

.5°l85 

•3*49 

.485 

•54223 

.2869 

73 

4185.39 

•725 

•57"3 

.2685 

.265 

•51383 

-3063 

J583 

•55421 

.2791 

74 

4300.84 

.828 

.58294 

.2612 

•355 

•52565 

.2981 

.682 

.56603 

.2716 

75 

4417.86 

3-932 

0.59460 

•2543 

3-446 

0-53731 

.2902 

3.782 

0.57769 

.2644 

76 

4536-46 

4-037 

.60611 

.2477 

•538 

.54881 

.2826 

.883 

.58919 

.2575 

4656.63 

.144 

.61746 

.2413 

.632 

.56017 

.2753 

.986 

.60056 

.2509 

78 

4778.36 

•253 

.62867 

•2351 

•727 

•57137 

.2683 

4.090 

.61175 

•2445 

79 

4901.67 

•362 

•63974 

.2292 

•823 

.58244 

.2615 

.177 

.62283 

•2394 

80 

81 
82 

83 

84 

5026.55 
5'  53-oo 
5281.02 
5410.61 
5541-77 

4-474 
.586 
.700 
.815 
•932 

0.65066 
•66145 
.67211 
.68264 
.69304 

•2235 
.2180 
.2128 
.2077 
.2027 

3.921 
4.019 
.119 

.220 
•323 

0.59336 
.60415 
.61481 
•62534 
.63574 

•2550 
.2488 
.2428 
•2369 

4-303 
.411 
.521 
.631 

-744 

0.63375 
•64454 
•65519 
-66572 
.67612 

•2324 
.2267 

.2212 
.2159 
.2108 

85 

86 

87 
88 

89 

5674-50 
5808.80 
5944-68 
6082.12 
6221.14 

5-050 
.170 
.291 
•413 

•537 

0.70332 
•71348 
•72352 
•73345 
•74326 

.1980 

•1934 
.1890 
.1847 
.1806 

4.426 
•531 
•637 
•744 
.852 

0.64602 
.65618 
.66622 
.67615 
.68596 

.2259 
.2207 
.2157 
.2108 
.2061 

4-857 
•972 

.206 
•325 

0.68640 
•69656 
.70660 

•71653 
.72634 

.2059 
.2011 
.1965 
.1921 
.1878 

90 

92 
93 
94 

6361.73 
6503.88 
6647.61 
6792.91 
6939.78 

5.662 
.788 
.916 
6.046 
.176 

0.75297 
.76256 
.77206 
.78144 
•79074 

.1766 
.1728 
.1690 
.1654 
.1619 

4.962 

5-073 
.183 
.298 
-413 

0.69567 
.70527 
.71476 
.72414 
•73344 

.2015 
.1971 
.1929 
.1887 
.1847 

5?7 
.690 

.815 
•940 

0.73605 
.74565 
.755*4 
•764^2 

.1836 
.1796 

•1757 
.I72O 
•1683 

95 

96 
97 
98 
99 

7088.22 
7238.23 
7389.81 

6.309 
.442 

•577 
.713 
.851 

0-79993 
.80902 
.81802 
.82693 
.83575 

•1585 
•1552 
.1520 
.1490 
.1460 

.646 
.764 
.884 
6.004 

0.74263 
•75*73 
•76073 
.76964 
.77846 

.1809 

.1771 

•1735 
.1670 
.1665 

6.068 
.196 
•326 
•457 
.589 

0.78301 
.79211 
.80111 
.81002 
.81884 

.1648 
.l6l4 
.1581 

:!£! 

100 

7853-98 

6.990 

0.84448 

•1431 

6.126 

0.78718 

.1632 

6.723 

0.82756 

.1487 

SMITHSONIAN  TABLES. 


47 


TABLE  59. 


BRITISH    AND    METRIC    UNITS, 

Cross  sections  and  weights  of  wires. 


The  cross  section  and  the  weight,  in  different  units,  of  Aluminium  wire  of  the  diameters  given  in  the  first  column, 
For  one  tenth  the  diameter  divide  sections  and  weights  by  100.  For  ten  times  the  diameter  multiply  by  100 
and  so  on. 


e 
'"j» 

Ji 

Area  of 
cross 
section 

Sq.  Mils. 

Aluminium  —  Density  2.67. 

Pounds 
per 
Foot. 

Log. 

Feet 
per 
Pound. 

Ounces 
per 
Foot. 

Log. 

Feet 
per 
Ounce. 

Grammes 
per 

Metre.* 

Log. 

Metres 
per 
Gramme. 

10 

78.54 

.0000909 

5.95862 

IIOOO. 

.001455 

3.16274 

687.5 

.02097 

2.32160 

47.69 

ii 

95-°3 

OIIOO 

4.04139 

9091. 

01760 

•24551 

602.4 

•02537 

•40437 

39-41 

12 

113.10 

01309 

.11699 

7638. 

0209^ 

.32111 

477-4 

.03020 

•47997 

33-  " 

J3 

132-73 

01536 

.18650 

6509. 

02458 

.39062 

406.8 

•03544 

.54948 

28.22 

14 

153-94 

01782 

.25088 

5612. 

02851 

.45500 

350.8 

.04110 

.61386 

24-33 

15 

176.71 

.OOO2O45 

4.31079 

4889. 

.003273 

3-5I49I 

305-6 

.04718 

2.67377 

21.19 

16 

201.06 

02327 

.36685 

4297. 

03724 

•57097 

268.5 

.05368 

.72984      18.63 

I7 

226.98 

02627 

.41952 

3876. 

04204 

.62364 

237-9 

.06060 

•78250 

16.50 

18 

254-47 

02946 

.46917 

3395- 

04713 

.67329 

212.2 

.06794 

.83215 

14.72 

19 

283-53 

03282 

•5l6i3 

3047. 

05251 

.72025 

190.4 

•07570 

.87911 

13.21 

20 

314.16 

.0003636 

4.56068 

2750. 

.005818 

3.76480 

I7I.9 

.08388 

2~.92366 

11.922 

21 

346.36 

04009 

.60306 

2494. 

06415 

.80718 

'55-9 

.09248 

_.966o4 

10.813 

22 

380.13 

04400 

.64346 

2273. 

07040 

.84758 

142.0 

.10149 

i  .00644 

9-853 

23 

415.48 

04809 

.68208 

2079. 

07697 

.88630 

129.9 

.11093 

.04506 

9.014 

24 

452.39 

05237 

.71904 

I9IO. 

08378 

.92316 

119.4 

.12079 

.08202 

8.279 

25 

26 

490.87 
530-93 

.0005682 
06147 

4-75450 
.78867 

1760. 
1627. 

.00909 
0983 

3.95862 
.99269 

IIO.OO 

101.70 

.1311 
.1418 

1.11748 
•*S1SS 

7.b30 

7-054 

27 

28 

572-56 
6i5-75 

06628 
07127 

•82135 
•85293 

1509. 
1403. 

1060 
1140 

2.02547 
•05705 

94-30 

87.69 

.1529 
.1644 

.184331     6.541 
.21592       6.083 

29 

660.52 

07646 

.88341 

I308. 

I223 

•08753 

81.75 

.1764 

.24640 

5.670 

30 

706.86 

0008182 

4.91286 

1222. 

.01309 

2.11698 

76.39 

.1887 

1.27584 

5-299 

3i 

754-77 

08737 

.94134 

"45- 

1398 

.14546 

71.54 

.2015 

•30433 

4.962 

32 

804.25 

09309 

.96892 

1074. 

1489 

•I73°4 

66.89 

.2147 

•33I9° 

.657 

33 

855-30 

09900 

•99563 

1010. 

'£4 

.19977 

63-13 

.2284 

•35863 

•379 

34 

907.92 

10509 

3.02158 

952. 

1681 

•22570 

59-47 

.2424 

•38456 

.125 

35 

36 

962.11 
1017.88 

OOIII4 
1178 

3.04675 
.07123 

897.9 
848.8 

.01782 
1885 

2.25087 

•27535 

56.12 

53-05 

.2569 
.2718 

1.40973 
.43421 

3-893 

37 

1075.21 

1245 

.09502 

803.5 

1991 

.29914 

50.22 

.2871 

.45800 

•483 

38 

1134.11 

1316 

.11918 

760.0 

2105 

.32329 

47-5° 

-3035 

.48216 

.295 

39 

1194.59 

1383 

•14075 

723.2 

2212 

•34487 

45-20 

.3190 

•50373 

.135 

40 

1  256.64 

001455 

3.16275 

687.5 

.02327 

2.36687 

42.97 

•3355 

T-52573 

2.980 

4i 
42 

1320.25 
138544 

I|28 
1604 

.18419 
.20512 

654.4 
623.6 

2445 

-38831 
.40924 

40.90 
38.97 

•3525 
•3699 

•54717 
.56810 

-837 
.704 

43 

1452.20 

1681 

.22556 

594.9 

2690 

.42968 

37-iS 

•3877 

.58854 

•579 

44 

1  520.53 

1760 

•24552 

568.2 

28l6 

.44964 

35-51 

.4060 

.6085! 

•463 

45 

1590.43 

001841 

3.26504 

543-2 

.02946 

2.46916 

33-95 

.4246 

1.62803 

2-355 

46 

1661.90 

1924 

.28413 

519.8 

3078 

.48825 

32-49 

•4437 

.64712 

•254 

47 

1734.94 

2008 

.30281 

498.0 

3213 

•50693 

31.12 

.4632 

.66580 

-!59 

48 

1809.56 

2095 

.32110 

4774 

3351 

.52522 

29.84 

.4832 

.68408 

.070 

49 

1885.74 

2183 

•33901 

458.1 

3492 

•54313 

28.63 

•5°35 

.70199 

1.986 

50 

1963.50 

002273 

3-35656 

440.0 

.03636 

2.56068 

27.50 

.5243 

^•7r954 

1.907 

5i 
52 

2042.82 
2123.72 

5?     « 

2365 
2458 

•37376 
•39063 

422.9 
406.8 

3783 

3933 

•57788 
•59475 

26.43 
25.42 

-5454 
•5670 

•73674 
•7536i 

•833 
.764 

53 

2206.18 

2554 

.40717 

394-2 

4086 

.61129 

24.47 

.5891 

•77015 

.698 

54 

2290.22 

2651 

.42341 

377-2 

4242 

•62753 

23-57 

.6115 

•78639 

•635 

55 

2375-83 

002750 

3-43934 

363-6 

.04400 

2.64346 

22.73 

•6343 

1.80233 

I-576 

SMITHSONIAN  TABLES. 


*  Diameters  and  sections  in  terms  of  thousandths  of  a  centimetre. 


48 


TABLE  59. 


BRITISH   AND   METRIC   UNITS. 

Cross  sections  and  weights  oi  wires. 


J* 

Area  of 

cross 
section 
in 
Sq.  Mils. 

Aluminium  —  Density  2.67. 

Pounds 
per 
Foot. 

Log. 

Feet 
per 
Pound. 

Ounces 
per 
Foot. 

Log. 

Feet 
per 
Ounce. 

Grammes 
per 

Metre.* 

Log. 

Metres 
per 
jramme. 

55 

56 

2463.01 

.002750 
2851 

3-43934 
•45500 

350^8 

.04400 
.04562 

2.64346 
.65912 

22.73 
21.92 

0.6343 
.6576 

1.80233 
.81798 

1.576 
.521 

57 

255^76 

2954 

•47037 

338.6 

.04726 

.67449 

2I.I6 

•6813 

•83335 

.468 

58 

2642.08 

3058 

•48547 

327.0 

.04893 

.68959 

20.44 

•7054 

.84846 

.418 

59 

2733-97 

3^5 

.50032 

316.0 

.05063 

.70444 

'9-75 

.7300 

•86331 

•370 

60 

2827.43 

•003273 

3.51492 

305-5 

.05236 

2.71904 

19.10 

0-7549 

1.87790 

1.325 

61 

2922.47 

3383 

.52928 

•05413 

•73340 

18.48 

.7803 

.89226 

.282 

62 
63 

3019.07 

$8 

•54340 
•5573° 

277.1 

•05591 
•05773 

•74752 
.76142 

17.88 
17-32 

.8061 
•8323 

.90638 
.92028 

.241 
.2OI 

64 

3216.99 

3724 

.57098 

268.5 

•05958 

•77510 

16.78 

8589 

•93396 

.164 

65 

33I8.3I 

.003841 

3-58445 

260.3 

.06146 

2.78857 

16.27 

0.8860 

T.94743 

I.I29 

66 

3421.19 

3960 

•59771 

252-5 

.06336 

.80183 

15-78 

•9J35 

.96069 

•095 

67 

4081 

.61077 

245.0 

.06530 

.81489 

'5-31 

•94i3 

•97375 

.062 

68 

3631.68 

4204 

.62364 

237-9 

.06726 

•82777 

14.87 

•9697 

.98662 

.031 

69 

3739-28 

4328 

.63632 

231.0 

.06925 

.84044 

14.44 

.9984 

•99930 

.OO2 

70 

3848.45 

•004456 

3-64893 

224.4 

.07129 

2.85305 

14.03 

1.028 

0.01191 

0.9730 

71 

3959.19 

4583 

.66114 

218.2 

•07333 

.86526 

13.64 

•057 

.02412 

.9460 

72 

4071.50 

.67328 

212.2 

•07541 

.87740 

13.26 

.087 

.03627 

.9199 

73 
74 

4185.39 
4300.84 

4845 
4978 

.68526 
.69708 

206.4 
200-9 

•07751 
.07965 

•88938 
.90120 

12.90 
12-55 

.117 

.148 

.04825 
.06006 

.8949 
.8708 

75 

4417-86 

.005114 

3.70874 

I95.5 

.08182 

2.91286 

12.22 

1.180 

0.07172 

0.8477 

76 

453646 

525r 

•72025 

190.4 

.08402 

•92437 

II.9O 

.211 

.08323 

.8256 

77 
78 

4656.63 
4778.36 

5390 

.73160 
.74281 

185.5 
I80.8 

.08624 
.08850 

•93572 
.94693 

1  1.  60 
11.30 

•243 
.276 

.09458 
.10579 

.8043 
.7838 

79 

4901.67 

5674 

•75387 

176.2 

.09078 

•95799 

11.02 

•309 

.11686 

.7641 

80 

5026.55 

.005818 

3.76480 

I7I.9 

.09309 

2.96892 

10.742 

1.342 

0.12778 

0.7451 

81 
82 

5  i  53-oo 
5281.02 

5965 
6113 

•77559 
•78625 

167.6 
163.6 

.09544 
.09781 

.97971 
.99037 

10.479 
10.224 

•376 
.410 

•13857 
.14923 

.7092 

83 
84 

5410.61 
5541-77 

6263 
6415 

•79678 
.80718 

159-7 

.10021 
.10264 

i  .00090 
.01130 

9-979 
9-743 

•445 
.480 

.15976 
.17016 

.6922 
•6757 

85 

1    86 

5674.50 
5808.80 

.006568 
6724 

3.81746 
.82762 

152.2 

148.7 

.IO5I 
.1076 

1.02158 
•03174 

9-295 

1.5^5 
.551 

0.18044 
.19060 

0.6600 
.6448 

87 
88 

5944-68 
6082.12 

6881 
7040 

.83766 
.84758 

145-3 
142.0 

.IIOI 
.1126 

.04178 
.05170 

9.082 
8.878 

.624 

.20064 
.21057 

.6300 
.6158 

89 

6221.  14 

7201 

.85740 

138.9 

.1152 

.06152 

8.679 

.661 

.22038 

.6020 

90 

92 

6361-73 
6503.88 
6647.61 

.007364 
7528 
7695 

3.86710 
.87670 
.88619 

135-8 
132.8 
130.0 

.1178 

.I2O5 
.1231 

1.07122 
.08082 
.09031 

8.488 
8.302 

8.122 

1.699 

•737 

•775 

0.23009 
.23968 
.24918 

0.5887 

•5759 
•5634 

93 
94 

6792.91 
6939.78 

7863 
8033 

•89558 

127.2 
124.5 

.1258 
.1285 

.09970 
.10899 

7-949 
7.780 

.814 
•853 

.25856 
.26786 

•55'4 

•5397 

95 

7088.22 

.008205 

3.91407 

I2I-9 

.I3!3 

1.11819 

7.617 

1.893 

0.27705 

0.5284 

96 

7238.23 

8378 

*J  s     ~     * 

.92316 

1194 

.1341 

.1272? 

7-459 

•933 

.28614 

•5*74 

97 

7389.81 

8554 

.93216 

116.9 

.1369 

.13628 

7.307 

•973 

.29514 

.5068 

98 
99 

7542.96 
7697.69 

8731 
8910 

.94107 
•94989 

II2.2 

•1397 
.1426 

•i45J9 
.15401 

7-I58 
7-oi5 

2.014 
•055 

'.31287 

•4965 
.4865 

100 

7853.98 

.009091 

3.95862 

IIO.O 

•1455 

1.16274 

6.875 

2.097 

0.32160 

0.4769 

*  Diameters  and  sections  in  terms  of  thousandths  of  a  centimetre. 


SMITHSONIAN  TABLES. 


49 


TABLE  60. 


BRITISH    AND    METRIC    UNITS, 


Cross  sections  and  weights  of  wires. 

The  cross  section  and  the  weight,  in  different  units,  of  Platinum  wire  of  the  diameters  given  in  the  first  column. 
For  one  tenth  the  diameters  divide  sections  and  weights  by  100.     ft  or  ten  times  the  diameter  multiply  by  100, 


and  so  on. 


is 

Q 

Area  of 
cross 
section 
in 
Sq.  Mils. 

Platinum  —  Density  21.50. 

Pounds 
per 
Foot. 

Log. 

Feet 
per 
Pound. 

Ounces 
per 
Foot. 

Log. 

Feet 
per 
Ounce. 

Grammes 
per 
Metre.* 

Log. 

Metres 
per 
Gramme. 

10 

78.54 

.0007321 

4.86455 

1366.0 

.01171 

2.06867 

85.38 

0.1689 

7.22753 

5.922 

I 

95-°3 

008858 

•94732 

1  1  29.0 

.01417 

•I5H4 

70.56 

.2043 

.31030 

4.894 

12 

113.10 

01054 

3.02292 

948.6 

.01687 

.22704 

59-29 

.2432 

.38590 

4-II3 

13 
14 

132.73 
153-94 

01237 
01435 

.09243 
.15681 

808.3 
696.9 

•01979 
.02296 

•29655 
.36093 

50.52 
43-56 

•2854 

•33  10 

•45541 

•5'979 

3-504 
3-O2I 

15 

176.71 

.001647 

3.21672 

607.1 

.02635 

•2.42084 

37-95 

0.3799 

7-57970 

2.632 

16 

201.06 

01874 

.27278 

533-6 

.03005 

.47790 

33-27 

•4323 

•63576 

2.3II 

17 

226.98 

02II6 

.32544 

472.7 

•03385 

•52956 

29-54 

.4880 

.68843 

2.049 

19 

254-47 
283-53 

02372 
02643 

•37509 
.42206 

421.6 

378.4 

•03795 
.04228 

•57921 
.62618 

26-35 
23.65 

•5471 
.6096 

.73808 
.78504 

1.828 
1.640 

20 

314.16 

.002928 

3.46661 

341-5 

.04685 

2.67073 

21.34 

0.6754 

7.82959 

1.481 

21 

346-36 

03228 

.50898 

309-7 

.05165 

.71310 

19.36 

•7447 

.87197 

•343 

22 

380.13 

03543 

282.2 

.05669 

•75351 

17.64 

•8i73 

•9I237 

.224 

23 
24 

415.48 
452.39 

03873 
04217 

fioi 
497 

258.2 
237.2 

.06196 
.06747 

•79213 
.82909 

16.14 

14.82 

•8933 
.9726 

.95099 
•98795 

.119 
.028 

25 

490.87 

•004575 

3.66042 

218.6 

.07321 

2.86454 

13.66 

1.055 

0.02341 

0-9475 

26 

530-93 

04949 

.69449 

202.  i 

.07918 

.89861 

12.63 

.142 

•05748 

.8760 

27 

572-56 

05324 

.72628 

187.8 

•08539 

.93140 

11.71 

.231 

.09026 

.8124 

28 

05739 

.75886 

174.2 

.09183 

.96298 

10.89 

•324 

.12184 

•7553 

29 

660.52 

06157 

•78934 

162.4 

.09851 

.99346 

10.15 

.420 

.15232 

.7042 

30 

706.86 

.006589 

3.81879 

151.8 

.1054 

1.02291 

9.486 

1.520 

0.18177 

0.6580 

31 

754-77 

07035 

.84727 

142.1 

.1126 

.05139 

8.884 

•623 

.21025 

.6162 

32 

804.25 

07496 

.87485 

T33-4 

.1199 

•07897 

8.338 

•729 

•23783 

•5783 

33 

855-30 

07972 

•90157 

125.4 

.1276 

.10569 

7.840 

•839 

.26456 

•5438 

34 

907.92 

08463 

.92750 

118.2 

•1354 

.13162 

7.385 

•952 

.29049 

•5123 

35 

962.11 

.008968 

3.95268 

111.52 

•1435 

1.15680 

6.970 

2.069 

.031566 

0.4834 

36 

1017.88 

09488 

•97715 

105.41 

.1518 

.18127 

6.588 

.188 

.34014 

•4569 

37 

1075.21 

IOO22 

2.00095 

99.78 

.1604 

.20507 

6.236 

.312 

•36393 

.4326 

38 
39 

1134.11 
1194.59 

10595 
IH34 

.02511 
.04668 

94-38 
89.81 

.1695 
.1782 

.22923 
.25080 

5-899 

444 
.568 

.38809 
.40966 

.4092 
.3893 

40 

1256.64 

.01171 

1.06867 

85.38 

.1874 

1.27279 

5-336 

2.702 

0.43166 

0.3701 

41 

1320.25 

I23I 

.09011 

81.26 

.1969 

.29423 

5-079 

•839 

•45309 

•3523 

i    42 

I385-44 

1291 

.11104 

77-44 

.2066 

•3r5l6 

4.840 

-979 

•47403 

•3346 

1452.20 

1354 

.13148 

73.88 

.2166 

•33560 

4.617 

3.122 

.49446 

.3203 

44 

1  520.53 

1417 

•I5I45 

70.56 

.2268 

•35557 

4.410 

.269 

•51443 

.3059 

45 

1590.43 

.01482 

2.17097 

67.46 

.2372 

7.37509 

4.216 

3419 

0-53395 

0.2924 

46 

1661.90 

1549 

.19006 

64.56 

.2478 

.39418 

4-035 

•573 

•55304 

.2799 

47 

1734-94 

I6l7 

.20874 

61.84 

.2587 

.41286 

3-865 

•730 

•57172 

.2681 

48 

1809.56 

1687 

.22703 

59-29 

.2699 

•43"5 

3-705 

.891 

.59001 

.2570 

49 

1885.74 

1758 

.24494 

56.89 

.2812 

.44906 

3-556 

4-054 

.60792 

.2467 

50 

1963.50 

.01830 

2.26249 

54-64 

.2928 

1.46661 

3-4I5 

4.222 

0.62547 

0.2369 

51 

2042.82 

1904 

.27969 

52-52 

•3°47 

.48381 

3.282 

•392 

.64267 

.2277 

52 

2123.72 

1979 

•29655 

50-52 

•3*67 

•50067 

.566 

•65954 

.2190 

53 

2206.18 

2056 

•31310 

48.63 

.3290 

.51722 

3-039 

•743 

.67608 

.2108 

54 

2290.22 

2135 

•32933 

46.84 

•3415 

•53345 

2.928 

.924 

.69232 

.2031 

55 

2375.83 

.02214 

2.34527 

45.16 

•3543 

7-54939 

2.822 

5.108 

0.70825 

0.1958 

SMITHSONIAN  TABLES. 


Diameters  and  sections  in  terms  of  thousandths  of  a  centimetre. 
50 


TABLE  6O. 


BRITISH    AND   METRIC   UNITS. 

Cross  sections  and  weights  of  wires. 


•3, 

II 

Q 

Area  of 
cross 
section 
in 

Sq.  Mils. 

Platinum  —  Density  21.50. 

Pounds 

£5. 

Log. 

Feet 
per 
Pound. 

Ounces 
per 
Foot. 

Log. 

Feet 
per 
Ounce. 

Grammes 
per 
Metre.* 

Log. 

Metres 
per 
Gramme. 

55 

2375-83 

.O22I4 

2.34527 

45.16 

0-3543 

^•54939 

2.822 

5.108 

0.70825 

.1958 

56 

2463.01 

2296 

.36092 

43-56 

•3673 

•56504 

.722 

•295 

.72390 

.1888 

57 

2551.76 

23/8 

•37630 

42.04 

.3806 

.58042 

.628 

.486 

.73928 

.1823 

58 

2642.08 

2463 

.39140 

40.61 

•3940 

•59552 

•538 

.680 

•75438 

.1760 

59 

2733-97 

2548 

.40625 

39-24 

.4077 

.61037 

•453 

.878 

.76923 

.I7OI 

60 

2827.43 

.02635 

2.42085 

37-94 

0.4217 

1.62497 

2.372 

6.079 

0.78383 

.1645 

61 

2922.47 

2724 

•43521 

36.71 

•4358 

•63933 

•294 

•283 

.79819 

.1592 

62 

3019.07 

2814 

•44933 

35-54 

.4502 

•65345 

.221 

.491 

.81231 

•1541 

63 
64 

3u7-25 
3216.99 

2906 
2999 

•46323 
.47691 

34-42 
33-35 

.4649 
.4798 

•66735 
.68103 

'.084 

.702 
.917 

.82621 
.83989 

.1492 
.1446 

65 

33l8-3I 

•03093 

2.49037 

32-33 

0.4949 

1.69449 

2.O2I 

7-134 

0.85336 

.1402 

66 

3421.19 

3l89 

•50363 

31-36 

.5102 

•70775 

1.960 

.356 

.86662 

.1360 

67 
68 

3525-65 
3631.68 

3286 

3385 

.51670 
•52956 

30-43 
29-54 

.5258 
,5416 

.72082 
•73368 

.902 
.846 

:& 

.87968 

.89255 

.!3J9 
.1281 

69 

3739-28 

3485 

.54224 

28.69 

•5577 

•74636 

•793 

8.039 

•90523 

.1244 

70 

7i 

384845 
3959-  1  9 

.03588 
3690 

2.55485 
•56706 

27-87 
27.10 

o.574i 

•5904 

^•75897 
.77118 

1.742 
.694 

8.276 
•5^2 

0.91784 

.93004 

.1208 
•"75 

72 

4071.50 

3795 

•57921 

26-35 

.6072 

•78333 

.647 

.754 

.94219 

.1142 

73 

4185.39 

3901 

•59"9 

25-63 

.6242 

•79531 

.602 

•999 

•95417 

.IIII 

74 

4300.84 

4009 

.60301 

24-95 

.6414 

.80713 

•559 

9.247 

.96599 

.1081 

75 

4417.86 

.04118 

2.61467 

24.28 

0.6589 

1.81879 

1.518 

9.498 

0.97765 

.10528 

76 

4536-46 

4228 

.62617 

23-65 

•6765 

.83029 

478 

9-753 

.98916 

•I02S 

77 

4656.63 

4340 

•63753 

23.04 

.6945 

.84165 

.440 

IO.OI2 

1.00051 

.09988 

78 

4778.36 

4454 

.64874 

22.45 

.7126 

.85286 

•403 

10.273 

.01172 

•°9734 

79 

4901.67 

4569 

.65980 

21.89 

•7310 

.86392 

.368 

»0.539 

.02278 

.09489 

80 

5026.55 

.04685 

2.67073 

21.34 

0.7496 

1.87485 

1-334 

I0.8I 

1.03371 

.09253 

81 

5I53-°° 

4803 

.68152 

20.82 

•7685 

.88564 

.301 

1  1.  08 

.04450 

.09026 

no 

82 

5281.02 

4922 

.69217 

20.32 

.7876 

.89629 

.270 

n-35 

•°^o 

.08807 

83 
84 

5410.61 

5541-77 

5043 
5165 

.70270 
.71310 

19.83 
19.36 

.8069 
.8265 

.90682 
.91722 

•239 
.210 

11.63 
11.91 

.06568 
.07609 

.08596 
•08393 

85 

86 

87 
88 

5674-5° 
5808.80 
5944-68 
6082.12 

.05289 
54i4 
554i 
5669 

2.72338 

•73354 
•74358 
•75351 

18.91 

18.47 
18.05 
17.64 

0.8463 
.8663 
.8866 
.9070 

1.92750 
.93766 
.94770 
.95763 

1.182 

•154 

.128 

.102 

I2.2O 
12.49 

12.78 
13.08 

1.08637 
.09652 
.10657 
.11649 

.08197 
.08007 
.07807 
.07647 

89 

6221.14 

5799 

•76333 

17-25 

.9278 

.96745 

.078 

13-37 

.12631 

•07477 

90 

9i 
92 

93 
94 

6361.73 

6503.88 
6647.61 
6792.91 
6939.78 

•05930 
6062 
6196 
6332 
6469 

2.77303 
•78263 
.79212 
.80151 
.81080 

16.86 
16.50 
16.14 

15-79 
15.46 

0.9487 
.9699 
.9914 
1.0130 
.0350 

1.97715 
.98675 
.99624 
0.00563 
.01492 

I.054I 
.0310 
.0087 
0.9871 
.9661 

13.68 
13.98 
14.29 
14.60 
14.92 

1.13601 

.14561 

.15510 
.16449 
•17378 

.07311 
.07152 
.06997 
.06847 
.06702 

95 

96 

97 
98 

99 

7088.22 
7238-23 
7389.81 
7542.96 
7697.69 

.06607 

6747 
6888 

7031 

7i75 

2.81999 
.82909 
.83809 
.84700 
.85582 

15.14 

14.82 

H-S2 
14.22 

13-94 

1.057 
.079 
.102 

.148 

0.0241  1 
.03321 
.04221 
.05112 
.05994 

0.9460 
.9264 
.9074 
.8890 
.8711 

15.24 
I5-56 
I5-89 
16.22 

16.55 

1.18298 
.19207 

.20107 
.20998 

.21880 

.06562 
.06426 
.06294 
.06166 
.06042 

100 

7853-98 

.07321 

2.86455 

13.66 

1.171 

0.06867 

0.8538 

16.89 

1.22753 

.05922 

*  Diameters  and  sections  in  terms  of  thousandths  of  a  millimetre. 


SMITHSONIAN  TABLES. 


TABLE  61. 


BRITISH    AND    METRIC    UNITS, 

Cross  sections  and  weights  of  wires. 


The  cross  section  and  the  weight,  in  different  units,  of  Gold  wire  of  the  diameters  given  in  the  first  column. 
For  one  tenth  the  diameters  divide  sections  and  weights  by  100.  For  ten  times  the  diameter  multiply  by  100. 
and  so  on. 


c 

"t_uj 

5>5 
2  ^ 

0 

Area  of 
cross 
section 
in 

Sq.  Mils. 

Gold  —  Density  19.30. 

Troy 
Ounces 
per  Foot. 

Log. 

Feet 
per  Troy 
Ounce. 

Grains 
per 
Foot. 

Log. 

Feet 
pei- 
Grain. 

Grammes 
per 
Metre.* 

Log. 

Metres 
per 
Gramme. 

10 

78.54 

.00958 

3.98152 

104-35 

4.600 

0.66276 

•2174 

0.1516 

1.18065 

6-597 

n 

95-03 

.OIl6o 

2.06429 

86.24 

5.566 

•74553 

.1797 

.1834 

.26342 

5-452 

12 

II3.TO 

.01380 

.13989 

72.46 

6.624 

.82114 

.1510 

.2183 

•33902 

4.581 

13 

132.73 

.01657 

.21940 

60.34 

7-774 

.89064 

.1286 

.2562 

•40853 

3-904 

14 

153-94 

.01878 

.27378 

53-24 

9.016 

.95503 

.1109 

.2971 

.47291 

3-366 

15 

1/6.71 

.02156 

2.33369 

46.38 

'0-35 

1.01493 

.09662 

0.3411 

1.53282 

2-932 

16 

2OI.O6 

•02453 

.38976 

40.76 

11.78 

.07100 

.08492 

.3880 

.58888 

•577 

i? 

226.98 

.02770 

.44242 

36.11 

13.29 

.12366 

.07522 

.4381 

.64154 

•283 

18 

254-47 

.03105 

.49207 

32.21 

14.90 

•I733I 

.06710 

.4911 

.69119 

.036 

19 

283.53 

.03460 

•53903 

28.90 

16.61 

.22027 

.06022 

•5472 

.73816 

1.827 

20 

314.16 

•03833 

2.58358 

26.09 

18.40 

1.26482 

•05435 

0.6063 

1.78271 

1.649 

21 

346.36 

.04226 

.62596 

23.66 

20.29 

.30720 

•04939 

.6685 

.82509 

•496 

22 

380.13 

.04638 

.66636 

21.56 

22.26 

-3476i 

.04492 

•7337 

.86549 

-363 

23 

415.48 

•04954 

.69498 

20.  1  8 

24-33 

.38622 

.04109 

.8019 

.9041  1 

.248 

24 

452-39 

•05520 

.74194 

18.12 

26.50 

.42319 

•03774 

•8731 

.94107 

•145 

25 

490.87 

.05990 

2.77740 

16.70 

28.75 

1.45865 

.03478 

0-9474 

1.97652 

f-0555 

26 

530-93 

.06478 

.81147 

15-44 

31.10 

.49271 

.03216 

1.0247 

0.01059 

0-9759 

27 

572.56 

.06986 

.84425 

I4-31 

33-53 

•52549 

.02982 

.1050 

•04338 

9050 

28 
29 

6I5-75 
660.52 

•075T3 
.08060 

.87584 
.90632 

J3-3' 

12.41 

36.06 
38.69 

.55708 
•58756 

.02773 
.02585 

.1884 
.2748 

.07496 
.10544 

.8415 
.7844 

30 

706.86 

.08625 

2-93577 

11-594 

41.40 

1.61701 

.02415 

1.364 

0.13489 

0-7330 

3i 

754-77 

.09210 

.96425 

10.858 

44.21 

.64549 

.02262 

•457 

•16337 

.6912 

32 

804.25 

.09813 

.99182 

10.190 

47.10 

•67306 

.02123 

.19095 

.6442 

33 

855-30 

.10436 

1.01855 

9.582 

50.09 

.69979 

.01996 

.651 

.21768 

.6058 

34 

907.92 

.11078 

.04448 

9.027 

53-i8 

•72572 

.Ol88l 

•752 

.24360 

•5707 

35 

962.11 

.1174 

1.06965 

8.518 

56.35 

1.75089 

•01775 

1-857 

0.26878 

0-5385 

36 

1017.88 

.1242 

.09413 

8.051 

59.62 

•77537 

.01677 

•965 

•29325 

.5090 

37 

1075.21 

.1312 

.11792 

7.622 

62.97 

.79917 

.01588 

2.070 

•3l6Q5 

.4830 

38 

1134.11 

•1387 

.14208 

7.210 

66.58 

.82332 

.01502 

.194 

.34121 

•4558 

39 

1194.59 

.1458 

•16365 

6.861 

69.97 

.84489 

.01429 

-306 

.36278 

•4337 

40 

1256.64 

•i|33 

7.18565 

6.521 

73.60 

1.86689 

•OI359 

2.425 

0.38478 

0.4123 

4i 

1320.25 

.1611 

.20709 

6.207 

77-33 

.88833 

.01293 

•548 

.4062  1 

•3924 

42 

I385-44 

.1691 

.22802 

5-9I5 

81.14 

.90926 

.01232 

.674 

•42715 

•3740 

43 

1452.20 

.1772 

.24846 

5-643 

85.05 

.92970 

.01176 

.803 

•44758 

•3568 

44 

1520.53 

•1855 

.26843 

5-390 

89.06 

.94967 

.01123 

•935 

•46755 

•3408 

45 

1590.43 

.1941 

1.28795 

5-153 

93-  1  5 

1.96919 

.010735 

3.070 

0.48707 

0.3258 

46 

1661.90 

.2028 

.30704 

4-93i 

97-34 

.98828 

.010273 

.207 

.50616 

.3118 

47 

1734-94 

.2117 

•32572 

4.724 

101.61 

2.00696 

.009842 

•348 

•52484 

.2986 

48 

1809.56 

.2208 

•34400 

4-529 

105.99 

.02525 

•009435 

.492 

•543J3 

.2863 

49 

1885.74 

•2301 

.36191 

4-346 

110.45 

•043  i  5 

.009054 

•639 

.56104 

-2748 

50 

51 

1963.50 
2042.82 

.2396 
•2493 

1.37946 
.39666 

4.174 
4.012 

115.0 
119.6 

2.06070 
.07790 

.008696 
.008358 

3-790 
•943 

0-57859 
•59579 

0.2639 

•2537 

52 

2123.72 

.2591 

•41353 

3-859 

124.4 

•09477 

.008039 

4.099 

.61265 

.2440 

53 

2206.18 

2692 

•43007 

3-7I5 

129.2 

.11131 

.007739 

.258 

.62920 

•2349 

54 

2290.22 

•2795 

.44631 

3-578 

i34-i 

•'2755 

•007455 

.420 

•64543 

.2262 

55 

2375-83 

.2899 

1.46225 

3-449 

139.2 

2-14349 

.007186 

4.585 

0.66137 

0.2181 

I 

SMITHSONIAN  TABLES. 


Diameters  and  sections  in  terms  of  thousandths  of  a  centimetre. 
52 


TABLE  61 


BRITISH   AND   METRIC    UNITS. 

Cross  sections  and  weights  of  wires. 


c 
""  <fl 

Is 

Area  of 
cross 
section 
in 

Sq.  Mils. 

Gold  —  Density  19.30. 

Troy 
Ounces 

Foot. 

Log. 

Feet 
per  Troy 
Ounce. 

Grains 
Foot. 

Log. 

Feet 
per 
Grain. 

Grammes 
per 
Metre.* 

Log. 

Metres 
per 
Gramme. 

55 

2375-83 

.2899 

1.46225 

3-449 

139.2 

2.14349 

.007186 

4.585 

0.66137 

.2l8l 

56 

2463.01 

•3005 

.47790 

.327 

14.4-3 

•i59I4 

6932 

4-754 

.67702 

.2104 

57 

2551.76 

•3JI4 

•49327 

.212 

149-5 

•I7451 

669I 

4-925 

.69240 

.2031 

58 

2642.08 

.3224 

.50838 

.IO2 

154-7 

.18962 

6462 

5-°99 

•7075° 

.1961 

59 

2733-97 

•3336 

•52323 

2.998 

1  60.  1 

.20447 

6245 

5.277 

•72235 

•l895  , 

60 

2827.43 

•3450 

T-53782 

2.899 

165.6 

2.21906 

.006039 

5457 

0.73695 

•1833 

6r 

2922.47 

.3566 

.55218 

.804 

I7I.2 

•23342 

5842 

5.640 

•7S*3l 

•1773 

62 
63 

3019.07 

3JI7-25 

.3684 
.3804 

.56630 
.58020 

'629 

176.8 
182.6 

•24754 
.26144 

5655 
5477 

5-827 
6.016 

•76543 
•77933 

.1716 
.1662 

64 

3216.99 

•3925 

.59388 

•548 

188.4 

.27512 

5307 

6.209 

•79301 

.1611 

65 

33*8.31 

.4049 

1.60735 

2.470 

194.4 

2.28859 

.005145 

6.404 

0.80647 

.1561 

66 

3421.19 

•4175 

.62061 

•395 

200-4 

•3OI85 

4991 

6.603 

•81973 

•i5H 

67 
68 

3525-65 
3631.68 

.4302 

4431 

•63367 
•64654 

•324 
•257 

206.5 
212.7 

•3J49i 

.32778 

4843 
4701 

6.805 
7.010 

.83280 
.84566 

.1470 
.1427 

69 

3739-28 

•4563 

•  .65922 

.192 

219.0 

.34046 

4566 

7.217 

-85835 

.1386 

70 

384845 

.4697 

1.67183 

2.129 

225-5 

2.35307 

•004435 

7.429 

0.87096 

.1346 

7i 

39  59-  i  9 

.4831 

.68404 

.070 

231.9 

-36528 

4312 

7.641 

.88316 

.1309 

72 

4071.50 

.4968 

.69619 

.013 

238.4 

•37743 

4195 

7.858 

.89531 

•1273 

73 

4185.39 

.5107 

.70817 

1.958 

245-1 

.38941 

4079 

8.078 

.90729 

.1238 

74 

4300.84 

.5248  . 

.71998 

•905 

251.9 

.40123 

3970 

8-301 

.91911 

.1204 

75 

4417-86 

•5391 

1.73164 

I-855 

258.8 

2.41288 

.003865 

8.526 

0.93077 

•1173 

76 

4536.46 

•5535 

-743r5 

.807 

265.7 

42439 

3764 

8-755 

•94227 

.1142 

77 

4656.63 

.5682 

•7545° 

.760 

272.7 

43574 

3666 

8.987 

•95363 

.1113 

78 

4778.36 

-5831 

•76571 

•715 

279.9 

44695 

3573 

9.222 

.96484 

.1084 

79 

4901.67 

.5981 

.77678 

.672 

287.1 

45801 

3483 

9.460 

•97590 

•1057 

80 

5026.55 

.6133 

1.78770 

1.630 

294.4 

2.46894 

.003401 

9.701 

0.98683 

.10308 

81 

5I53-°° 

.6288 

.79849 

•59° 

301.8 

47973 

33T3 

9-945 

.99762 

.10055 

82 

5281.02 

.6444 

.80915 

•552 

309.3 

.49039 

3233 

10.192 

1.00828 

.09812 

83 

5410.61 

.6602 

.81968 

•5*5 

316.9 

.50092 

3156 

10.442 

.01880 

•09577 

84 

554L77 

.6762 

.83008 

479 

324-6 

•5"32 

3081 

10.696 

.02921 

•09349 

85 

^674.50 

.6924 

1.84036 

1.444 

332-4 

2.52160 

.003009 

10.95 

1.03948 

.09131 

86 

5808.80 

.7088 

.85052 

.411 

340.2 

•53176 

2939 

II.  21 

.04964 

.08919 

87 

5944-68 

•7254 

.86056 

•379 

348.2 

.54180 

2872 

11.47 

.05969 

.08716 

88 

6082.12 

.7421 

.87049 

•347 

356.2 

•55J73 

2807 

11.74 

.06961 

•08519 

89 

6221.14 

•7591 

.88030 

•317 

3644 

•56154 

2744 

I2.OI 

.07943 

.08328 

90 

9i 
92 

93 
94 

6361.73 
6503.88 
6647.61 
6792.91 
6939.78 

•7763 
•7936 
.8111 
.8291 
.8468 

7.89001 
.89960 
.90910 
.91858 
•92778 

1.288 
.260 

.206 
.181 

372-6 
380.9 
389-3 
397-9 
406.5 

2.57125 
•58085 
•59034 
•59972 
.60902 

.002684 
2625 

256§ 

25i3 
2460 

12.28 

12-55 
12.83 
13.11 
13-39 

1.08913 

•09873 
.10822 
.11761 
.12690 

.08145 
.07967 
.07794 
.07628 
.07466 

95 

96 

97 
98 

99 

7088.22 
7238.23 
7389.81 
7542.96 
7697.69 

.8649 
.8832 
.9017 
.9204 
•9393 

1.93697 
.94606 
•955°7 
.96397 
.97279 

1.156 
.132 
.109 
.086 
.065 

415.2 

423-9 
432.8 
441.8 
45°-9 

2.61821 
.62731 

•63631 
.64521 

•65403 

.002409 

2359 
2310 
2263 
2218 

13.68 

13-97 
14.26 
14.56 
14.86 

1.13609 
.14519 

•I54I9 
.16310 
.17192 

.07310 
.07158 
.07011 
.06869 
•06731 

100 

7853-98 

•9583 

1.98152 

1.043 

460.0 

2.66276 

.002174 

I5.l6 

1.18065 

.06597 

SMITHSONIAN  TABLES. 


Diameters  and  sections  in  terms  of  thousandths  of  a  centimetre. 


53 


TABLE  62. 


BRITISH    AND    METRIC    UNITS. 

Cross  sections  and  weights  of  wires. 


The  cross  section  and  the  weight,  in  different  units,  of  Silver  wire  of  the  diameters  given  in  the  first  column.  Fo 
one  tenth  the  diameters  divide  the  section  and  weights  by  100.  For  ten  times  the  diameter  muliply  by  100,  am 
so  on. 


a 

I1 

Area  of 
cross 
section 

Sq/Mils. 

Silver  —  Density  10.50. 

Troy 
Ounces 
per  Foot. 

Log. 

Feet 
per  Troy 
Ounce. 

Grains 
Foot. 

Log. 

Feet 
per 
Grain. 

Grammes 
per 

Metre.* 

Log. 

Metres 
per 
Gramme. 

10 

78.54 

.005214 

3-717I5 

191.79 

2.503 

0.39839 

•3996 

0.08247 

2.91628 

12.126 

II 

95-°3 

.006308 

-79992 

158.52 

3.028 

.48117 

•3302 

.09978 

.99905 

10.022 

•  12 
13 
M 

113.10 
I32-73 
153-94 

.007508 
.OIO2I9 

•87553 
•94503 
2.00942 

I33-I9 
113-49 
97.86 

3.604 
4.229 
4.905 

.62627 
.69066 

•2775 
.2364 
•2039 

.11876 

•J3937 
.16164 

1.07465 
.14416 
.20854 

8.420 

m 

15 

176.71 

.01173 

2.06932 

85.24 

5.631 

0.75057 

.1776 

0.1855 

7.26845 

5-389 

16 

2OI.O6 

•OI335 

•12539 

74-92 

6.407 

.80663 

.1561 

.2111 

•32452 

4-737 

17 

226.98 

.01507 

.17805 

66.37 

7-233 

.85929 

•1383 

•2383 

•37718 

4.196 

18 

254.47 

.01689 

.22770 

59.20 

8.109 

.90894 

•I233 

.2672 

.42683 

3-743 

J9 

283-53 

.01882 

.27466 

53-  1  3 

9-034 

•9559° 

.1107 

•2977 

•47379 

3-359 

20 

314.16 

.02086 

2.31921 

47-95 

IO.OI 

1.00046 

.09990 

0.3299 

^•5*834 

3-031 

21 

346.36 

.02299 

•36159 

43-49 

II.O4 

.04283 

.09060 

•3637 

•56072 

2.750 

22 

380.13 

.02523 

.40200 

39-63 

12.  II 

.08324 

.08256 

•399r 

.60112 

•505 

23 

415.48 

.02758 

.44061 

36.26 

13.24 

.12186 

•07553 

•4363 

•63974 

.292 

24 

452-39 

.03003 

•47758 

32-99 

1442 

.15882 

.06937 

•475° 

.67670 

.105 

25 

490.87 

•03259 

2.51303 

30.69 

15.64 

1.19427 

.06425 

o.5i54 

7.71216 

1.940 

26 

530-93 

•03525 

.54710 

28.37 

16.92 

.22834 

.05911 

•5575 

.74623 

•794 

27 

572.56 

.03801 

.57988 

26.31 

18.24 

.26113 

.05481 

.6012 

.77901 

•663 

28 

6I5-75 

.04088 

.61147 

24.46 

19.62 

.29271 

.05097 

.6465 

.81059 

•547 

29 

660.52 

•04385 

.64195 

22.81 

2I.O5 

•32319 

•047  5  i 

•6935 

.84108 

.442 

30 

706.86 

.04692 

2.67140 

21.31 

22.52 

1-35264 

.04440 

0.7422 

7.87052 

1-347 

31 

754-77 

.05010 

.69988 

19.96 

24.05 

.38112 

0.4158 

•7925 

.89900 

.262 

32 
33 

804.25 
855-30 

•05339 
.05678 

•72745 
•75418 

18.73 
17.61 

25-63 

27.25 

.40870 
•43542 

0.3902 
0.3669 

•8445 
.8981 

.92658 
•9533  i 

.184 
•113 

34 

907.92 

.06027 

.7801  1 

16.59 

28-93 

•46135 

0-3457 

•9533 

•97924 

.049 

35 

962.11 

.06387 

2.80528 

15.66 

30.66 

1.48653 

.03262 

I.OIO 

0.00441 

0.9899 

36 

1017.88 

.06757 

.82976 

14.80 

32-43 

.51100 

.03083 

.069 

.02889 

.9356 

37 

1075.21 

.07138 

•85356 

14.01 

34.26 

.5348o 

.02919 

.129 

.05268 

.8857 

38 

1134.11 

.07546 

.87772 

13-25 

36.22 

.02761 

.194 

.07684 

.8378 

39 

1194.59 

.07930 

.89928 

12.61 

38.06 

•58052 

.02627 

•254 

.09841 

•7973 

40 

1256.64 

.08342 

2.92128 

11.99 

40.04 

1.60252 

.02497 

I-3I9 

0.12041 

0-7579 

4i 

1320.25 

.08764 

.94272 

11.41 

42.07 

.62396 

.02377 

.386 

.14185 

•7213 

42 

'  38  5-44 

.09197 

•96365 

10.87 

44.I5 

.64489 

.02265 

•455 

.16278 

•6874 

43 

1452.20 

.09640 

.98409 

Jo-37 

46.27 

•66533 

.02161 

•525 

.18322 

.6558 

44 

1520.53 

.10094 

1  .00406 

9.91 

48.45 

.68530 

.02064 

•597 

.20318 

.6263 

45 

1590.43 

.1056 

7.02358 

9.471 

50.68 

1.70482 

.01973 

1.670 

0.22270 

0.5988 

46 

1661.90 

.1103 

.04267 

9.065 

52.96 

•72391 

.01888 

•745 

.24179 

•5731 

47 

173494 

.1152 

;o6i35 

8.683 

55-28 

•74259 

.01809 

.822 

.26047 

•5489 

48 

1809.56 

.1201 

.07964 

8-325 

57-66 

.76088 

•01734 

.900 

.27876 

•5263 

49 

1885.74 

.1252 

•09755 

7.988 

60.09 

•77879 

.01664 

.980 

.29667 

.5050 

50 

5* 

1963.50 
2042.82 

•1303 
•1356 

7.11509 
.13229 

7.672 
7-374 

62.57 
65.09 

1.79634 
.8i354 

•01598 
•01536 

2.062 

•145 

0.31422 

•33*42 

0.4850 
.4662 

52 

2123.72 

.I4IO 

.14916 

7.093 

67.67 

.83040 

.01478 

.230 

.34829 

•4484 

53 

2206.18 

.1465 

.16570 

6.828 

70.30 

.84695 

.01422 

.316 

•36483 

•4317 

54 

2290.22 

.1520 

.18194 

6.578 

72.99 

.86328 

.01370 

•405 

.38107 

•4158 

55 

2375-83 

•1577 

7.19788 

6.340 

75-70 

1.87912 

.01321 

2-495 

0.39700 

0.4009 

*  Diameters  and  sections  in  terms  of  thousandths  of  a  centimetre. 
SMITHSONIAN  TABLES. 

54 


TABLE  62, 


BRITISH    AND    METRIC   UNITS. 

Cross  sections  and  weights  of  wires. 


c 

~es 

5  ^ 

p 

Area  of 
cross 
section 

Sq/Mils. 

Silver  —  Density  10.50. 

Troy 
Ounces 
>er  Foot. 

Log. 

Feet 
per  Troy 
Ounce. 

Grains 
Foot. 

Log. 

Feet 
per 
Grain. 

Grammes 
per 
Metre.* 

Log. 

Metres 
per 
Gramme. 

55 

2375-83 

0.1577 

T.i9788 

6-340 

75-70 

1.87912 

.01321 

2-495 

0-39700 

0.4009 

56 

2463.01 

•l635 

•21353 

.116 

78.48 

.89477 

1274 

.586 

.41266 

.3867 

57 

255L76 

.1694 

5.903 

81.31 

.91014 

1230 

.679 

.42803 

•3732 

58 

2642.08 

•1754 

.24401 

.701 

84.19 

•92525 

1188 

•774 

•443  1  4 

.3605 

59 

2733-97 

.1815 

.25886 

.510 

87.12 

.94010 

1148 

.87I 

•45798 

.3484 

60 

2827.43 

0.1877 

1.27346 

5-328 

90.09 

1.95470 

.OHIO 

2.969 

0.47258 

0-3368 

61 

2922.47 

.1940 

.28781 

•155 

93.12 

.96906 

1074 

3.069 

.48694 

•3259 

62 

3019.07 

.2004 

•3OI93 

4.990 

96.20 

.98318 

1040 

.170 

.50106 

•3*55 

63 

3"7-25 

.2069 

•31584 

•832 

99-33 

.99708 

1007 

•273 

.51496 

•3055 

64 

3216.99 

.2136 

.3295^ 

•683 

102.51 

2.01075 

0975 

.378 

.52864 

.2961 

65 

3318.31 

0.2203 

1.34298 

4.540 

105.7 

2.02422 

•009457 

3-484 

0.54211 

0.2870 

66 

3421.19 

.2271 

•35624 

•403 

109.0 

.03748 

09173 

-592 

•55537 

.2784 

67 

3525-65 

.2340 

.36930 

.273 

112.3 

•05054 

08903 

.702 

•56843 

.2701 

68 

3631.68 

.2411 

.38217 

.148 

"5-7 

.06341 

08642 

.813 

•58130 

.2622 

69 

3739.28 

.2482 

•39485 

.029 

119.1 

.07609 

08393 

.926 

•59398 

•2547 

70 

384845 

0-2555 

1.40746 

3-9I3 

122.7 

2.08870 

.008153 

4.042 

0.60659 

0.2474 

71 

3959-  1  9 

.2628 

.41967 

.805 

126.2 

.10091 

07926 

•157 

.61880 

.2406 

72 

4071.50 

.2703 

.43182 

.700 

129.7 

.11306 

07708 

•275 

•63094 

•2339 

73 

4185.39 

.2778 

.44380 

•599 

133-4 

.12504 

07498 

.395 

.64293 

.2275 

74 

4300.84 

.2855 

.45560 

•502 

137-0 

.13686 

07297 

.516 

•65474 

,2214 

75 

4417.86 

0.2933 

1.46728 

3.410 

140.8 

2.14852 

.007104 

4-639 

0.66640 

0.2156 

76 

4536-46 

.3011 

.47878 

.321 

144.6 

.16002 

06918 

763 

.67791 

.2099 

77 

3p    x   /*• 

4656.63 

.3091 

.49014 

•235 

148.4 

.17138 

06739 

.889 

.68926 

.2045 

78 

4778.36 

•3:72 

•50134 

.152 

152.3 

.18258 

06568 

5-017 

.70047 

•1993 

79 

4901.67 

.3254 

.51241 

•073 

156.2 

.19365 

06402 

.147 

-7II53 

•'943 

80 

5026.55 

0-3337 

i.52333 

2.997 

160.2 

2.20458 

.006243 

5.278 

0.72246 

°-'895 

81 

5153.00 

.3421 

•53412 

•923 

164.2 

•21537 

06090 

.411 

.73325 

.1848 

82 

5281.02 

•35°6 

.54478 

.852 

168.3 

.22602 

05942 

•545 

•74391 

.1803 

83 
84 

5410.61 
5541-77 

•3592 
•3679 

•55531 
•56571 

.784 
.718 

172.4 
176.6 

.23655 
.24695 

05800 

05663 

.681 
.819 

•75444 
.76484 

.1760 
.1719 

85 

86 

5674-50 
5808.80 

0.3767 
•3856 

7-57599 
•58615 

2.655 
•593 

180.8 
185.1 

2.25723 
.26739 

-005531 
05403 

5-958 
6.099 

0.77512 
.78528 

0.1678 
.1640 

87 

oo 

00 

5944-68 
6082.12 

.3946 
•4038 

'Jot? 

•534 
477 

189.4 
193.8 

•27743 
.28736 

05279 

05160 

.242 
.386 

•79532 
.80524 

.1602 
.1566 

89 

6221.14 

.4130 

.61593 

.421 

198.2 

.29717 

05045 

•532 

.81506 

•1531 

90 

91 
92 

93 
94 

6361.73 
6503.88 
6647.61 
6792.91 
6939.78 

0.4223 
.4318 
•4413 
•45°9 
.4607 

1.62564 
.63524 
.64473 
.65411 
.66341 

2.368 
.316 
.266 
.218 
.171 

202.7 
207.2 

2II.8 

216.4 

221.  1 

2.30688 
•31648 
.32597 

•33535 
•34465 

•004933 
04825 
04721 
04620 
04522 

6.680 
.829 
.980 
7-132 
.287 

0.82476 
.83436 
.84385 
.85324 
.86254 

0.1497 
.1464 

•M33 

.1402 
.1372 

95 

96 
97 
98 
99 

7088.22 
7238.23 
7389.81 
7542.96 
7697.69 

0.4705 
.4805 
.4906 
.5007 
.5110 

1.67260 
.68170 
.69070 
.69961 
.70842 

2.125 
.081 
.038 
1.997 
•957 

225.9 
230.6 

235.5 
240.4 

245-3 

2.35384 
.36294 
.37194 
.38085 

•38967 

.004428 
04336 
04247 
04161 
04077 

7-443 
.600 

•759 
.920 
8.083 

0.87173 
.88082 
.88982 
.89873 
.90755 

0.1344 
.1316 
.1289 
.1263 
.1237 

100 

7853-98 

0.5214 

7.7I7I5 

1.918 

250.3 

2.39839 

.003996 

8.247 

0.91628 

0.1213 

*  Diameters  and  sections  in  terms  of  thousandths  of  a  centimetre. 


SMITHSONIAN  TABLES. 


55 


TABLE  63. 


WEIGHT   OF   SHEET    METAL, 


II 

ss 


O   O   0   O   0 

o  o  o  o  o 

I 

0^2   lf°    r? 
1-1   N   ro  •<*•  >o 

O   LO  O  LOO 

ro  ro  Tf  T)-  LO 
^O  f^OO   ON  O 

O   O   0   O   O 

O    0   O   0   0 

"3 

O 

GNCO  r^  r^vO 
i—  i   ro  t-o  r^  O\ 

CO   <-<   -tf-  r^  O 

E 

O   O   O   O   O 

O   O   O   O   O 

i-O  O   ^^  O   ^^ 

O   '-O  O   LO  O 

dj 

M    ^-O  CO    O 

ci  vo  i^»  ON  "-H 

!_      _,      _      _      ^ 

£ 

t^  rf  i-  co  »n 

ci    ONO    ^O  O 

1 

3 

v£)   ro  O  O   f  O 
M   "ICO    O    ro 

O  O   to  O   r^ 

VO  CO   «   Tj-O 

I-H    P-I    M    M    N 

5? 

VO   N  CO   Tf  O 
LO  «  VO    d  CO 

vq  N  co  •*  q 

co  r^  m  TJ-  M 

m 

to  100  r^oo 

& 
5 

q  q  q  q  q 

o  o  o  o  o 

rj-  ron   «   d 
ro  n   H-I   O   ON 

u 

~   N   ro^- 

LOO  t^oo  co 

. 

0   O   O   O   O 

O   O   O   0   0 

jj 

CO  vD  Tf  ri   O 
r-^  vo  ro  M   ON 
w   n   ro  ro 

CO  O    -<t  N    O 
0   ri-  D    0  CO 
TJ-  LOO  r^  t->. 

&1I 

H««*r« 

(Q  t-^CO   ON  O 

SMITHSONIAN  TABLES. 


TABLE  64, 


WEIGHT  OF  SHEET   METAL. 


Cm 


'§  o- 


I 


0,0 


I* 


-a 

H 


rtOO  W  VO  O 
•4-vd  ON  w  rf 


vO  fO       O  vO  fO  O  ' 
i>  tp  fo  w  q\      r^.ioco£" 


tooo  1-1  -<f  r^  ON  n  "TOO 

Q   O  *«   M  wi-iMMM 

,  rf  M  00  to  N   ONVO   ro  O 

t-i  N  M  ro  TJ-  rh  »">vo  t^ 


N  ^o  tx.  O  w         ^J"  r^  ON  c^  ^* 

•^  ON  fOOO  fO       r>.  w  r-»  1-1  vD 

HH      N     ^"   tO  tv.  CO     O     M      CO  TJ- 


VON  ONOO  oo  oo  r>- 1-~ 
r^-vo  u->*3-  ro  M  w 
.  to  to  1-1  ON  i^  i-o  to 


ON 

L/"> 


ONOO  r 
oo  r^^O 
ro  r^  M 

O  O  O  O 


rj-  ro  w  M 


ON  -^-00  M 

1^  COOO  Tf 

M  vo  O  v> 

M  >-n  o  ^J" 


OOOOO  Q  +*  t-<  i-t  +* 
rovO  ONM^O  OOM-^-t^O 
vOMOO^Oi-i  r^^t-OvOfO 


oovofi'-'ON      1^-        -_-- 

^o  I-H   t>  rooo         •**•  O  vO   <^  t^- 

a»  SIM     ^-T^^o" 

v)   co  ro  TT" 


M 

TfOO  M  VO  O 
0  0  M.'-I  N 


r^co  ON  O 


SMITHSONIAN  TABLES. 


57 


TABLE  65. 


SIZE,   WEIGHT,   AND    ELECTRICAL 

Size,  Weight,  and  Electrical  Constants  of  pure  hard  drawn  Copper  Wire  of  different  numbers 
Size  and  Weight. 


Gauge 
Number. 

Diameter  in 
Inches. 

Square  of 
Diameter 
(Circular 
Inches). 

Section  in 
Sq.  Inches. 

Pounds 
Foot. 

Log. 

Feet 
per 
Pound. 

0000 

0.4600 

0.2116 

O.l662 

0.6412 

T.8070I 

1.560 

000 

oo 

.4096 
.3648 

.1678 

•I33I 

.1318 
.1045 

.5085 
•4033 

.70631 
.60560 

1.967 
2.480 

o 

•3249 

•1055 

.0829 

.3198 

.50489 

3.127 

1 

0.2893 

0.08369 

0.06573 

0.2536 

1.40419 

3-943 

2 

.2576 

.06637 

•05213 

.2011 

•30348 

4.972 

3 

.2294 

.05263 

.04134 

•J595 

.20277 

6.270 

4 

.2043 

.04174 

.03278 

.1265 

.10206 

7-905 

5 

.1819 

.03310 

.02600 

.1003 

.00136 

9.969 

6 

0.1620 

0.02625 

0.02062 

0.07955 

2.90065 

12-57 

7 

•1443 

.02082 

•01635 

.06309 

•79994 

15.85 

8 

.I285 

.01651 

.01297 

.05003 

.69924 

19.99 

9 

.1144 

.01309 

.01028 

.03968 

•59853 

25.20 

10 

.1019 

.01038 

.00815 

.03146 

.49782 

3I-78 

11 

0.09074 

0.008234 

0.006467 

0.02495 

2.39711 

40.08 

12 

.08081 

.006530 

.005129 

.01979 

.29641 

50-54 

13 

.07196 

.005178 

.004067 

.01569 

•19570 

63.72 

14 

.06408 

.004107 

.003225 

.01244 

.09499 

80.35 

15 

.05707 

.003257 

.002558 

.00987 

3.99429 

101.32 

16 

0.05082 

0.002583 

O.OO2O28 

0.007827 

3-89358 

127.8 

17 

.04526 

.002048 

.001609 

.006207 

.79287 

161.1 

18 

.04030 

.001624 

.001276 

.004922 

.69217 

203.2 

19 

•°3589 

.001288 

.OOIOI2 

.003904 

.59146 

256.2 

20 

.03196 

.001021 

.OOO8O2 

.003096 

•49075 

323-1 

21 

0.02846 

O.OOoSlOI 

0.0006363 

0.002455 

3-39004 

408.2 

22 

•02535 

.0006424 

.0005046 

.001947 

.28934 

5T3-6 

23 

.02257 

.0005095 

.OOO4OOI 

.001544 

.18863 

647.7 

24 

.02010 

.0004040 

•0003173 

.001224 

.08792 

816.7 

25 

.01790 

.0003204 

.0002517 

.00097  i 

4.98722 

1029.9 

26 

0.01594 

O.OOO254I 

0.0001996 

0.0007700 

4.88651 

1298. 

27 

.01419 

.0002015 

.OOOI  583 

.0006107 

.78580 

1638. 

28 

.01264 

.0001598 

.OOOI255 

.0004843 

.68510 

2065. 

29 
30 

.01126 
.01003 

.OOOI267 
.OOOIOO5 

.0000995 
.0000789 

.0003841 
.0003046 

•58439 
.48368 

2604. 
3283- 

31 

0.008928 

O.OOO0797O 

O.OOOO626O 

0.000241  5 

4.38297 

4140. 

32 

.007950 

.00006321 

.00004964 

.0001915 

.28227 

5221. 

33 
34 

.007080 
.006304 

.00005013 
.00003975 

.00003937 
.OOOO3I22 

.0001519 
.0001205 

.18156 

.08085 

6583. 
830  r. 

35 

.005614 

.00003152 

.OOOO2476 

.0000955 

5.98015 

10468. 

36 

0.005000 

O.OOOO25OO 

0.00001963 

0.00007576 

5-8/944 

13200. 

37 

•004453 

.00001983 

.OOOOI557 

.00006008 

•77873 

16644. 

38 

.003965 

.OOOOI372 

.OOOOI235 

.00004765 

.67802 

20988. 

39 

•003531 

.OOOOI247 

.00000979 

.00003778 

•57732 

26465. 

40 

.003145 

.00000989 

.OOOOO777 

.00002996 

.47661 

33372. 

SMITHSONIAN 


TABLE  65, 


CONSTANTS   OF   COPPER    WIRE. 

according  to  the  American  Brown  and  Sharp  Gauge.     British  Measure.    Temperature  o°  C.     Density  8.90. 

Electrical  Constants. 


Resistance  and  Conductivity. 

Gauge 

Number. 

Ohms 
Foot. 

Log. 

Feet 
Ohm. 

Ohms 
per 
Pound. 

Pounds 
per 
Ohm. 

0.00004629 

5-6655I 

2l6oi. 

O.OOOO72I9 

13852. 

OOOO 

.00005837 
.00007361 

.76622 
.86693 

I7I3I. 
13586. 

.OOOII479 
.00018253 

8712. 
5479- 

000 

00 

.00009282 

.96764 

10774. 

.00029023 

3445- 

0 

O.OOOII70 

4.06834 

8544. 

0.000461  5 

2166.8 

1 

.0001476 

.16905 

6775. 

.0007338 

1362.8 

2 

.0001861 

.26976 

5373- 

.OOI1668 

857.0 

3 

.0002347 

.37046 

4261. 

.0018552 

539-o 

4 

.0002959 

.47117 

3379- 

.0029499 

339-o 

5 

0.0003731 

4.57188 

2680. 

0.004690 

213.22 

6 

.0004705 

.67259 

2125. 

.007458 

134.08 

7 

•0005933 

77329 

1685. 

.011859 

84-32 

8 

.0007482 
.0009434 

.87400 
•97471 

J337. 
1060. 

.Ol88<7 
.029984 

53.03 
33-35 

9 

10 

O.OOII9O 

3-0754I 

840.6 

0.04768 

20.973 

11 

.001500 

.17612 

666.6 

.07581 

13.191 

12 

.001892 

.27683 

528.7 

.12054 

8.296 

13 

.002385 

•37753 

419.2 

.19166 

5.218 

14 

.003008 

.47824 

332-5 

.30476 

3.281 

15 

0-003793 

3-57895 

263.7 

0.4846 

2.0636 

16 

.004783 

.67966 

209.1 

•7705 

1.2979 

'Z 

.006031 

.78036 

165.8 

1.2252 

0.8162 

18 

.007604 

.88107 

i3i-5 

I.948I 

•5i33 

19 

.009589 

.98178 

104.3 

3.0976 

.3228 

20 

0.01209 

2.08248 

82.70 

4.925 

0.20305 

21 

•01525 

.18319 

65-59 

7.832 

.12768 

22 

.01923 

.28390 

52.01 

12-453 

.08030 

23 

.02424 
.03057 

.38461 
•48531 

41.25 
32.71 

19.801 
31.484 

.05051 
.03176 

24 
25 

0-03855 
.04861 

2.58602 
.68673 

25-94 
20.57 

50.06 
79.60 

0.019976 
.012563 

26 

27 

.06130 
.07729 

.78743 
.88814 

16.31 

12.94 

126.57 
201.26 

.007901 
.004969 

28 
29 

.09746 

.98885 

10.26 

32O.OI 

.003125 

3° 

0.1229 

1.08955 

8.137 

508.8 

0.0019654 

31 

•1550 

-I9S4 

.2464 
.3107 

.19026 
.29097 
.39168 
.49238 

6.452 
5*»7 

4.058 
3.218 

1  286.'  5 
2045.6 
3252.6 

.0012359 
.0007773 
.0004889 
.0003074 

32 
33 
34 

35 

0.3918 
.4941 
.6230 
.7856 
.9906 

7.59309 

.79450 
.89521 

•99592 

2-552 
2.024 
1.605 

1-273 
1.009 

^172. 
8224. 
13076. 
20792. 
33060. 

0.0001934 
.0001216 
.0000765 
.0000481 
j  .0000303 

36 

$ 

39 

40 

SMITHSONIAN  TABLES. 


59 


TABLE  66. 


SIZE,  WEIGHT,  AND    ELECTRICAL 

Size,  Weight,  and  Electrical  Constants  of  pure  hard  drawn  Copper  Wire  of  different  numbers 
Size  and  Weight. 


Gauge 
Number. 

Diameter  in 
Centimetres. 

Square  of 
Diameter 
(Circular 
Cms.). 

Section  in 
Sq.  Cms. 

Grammes 
ftfire. 

Log. 

Metres 
per 
Gramme. 

OOOO 

1.1684 

1.3652 

1.0722 

954-3 

2.97966 

0.001048 

000 

.0405 

.0826 

0.8503 

756.8 

.87896 

.001322 

00 
O 

0.9266 

.8251 

0.8586 
.6809 

•6743 
•5343 

600.  i 

475-9 

•77825 
•67754 

.001666 
.OO2  1  OI 

1 

0.7348 

0.5400 

0.4241 

377-4 

2-57684 

0.002649 

2 

•6544 

.4282 

.3363 

299-3 

•47613 

.003341 

3 

.5827 

•3396 

.2667 

•37542 

.004213 

4 

.5189 

.2693 

.2115 

188.2 

.27472 

.005312 

5 

.4621 

.2136 

.1677 

149-3 

.17401 

.006699 

6 

0.4115 

0.16936 

o.  1  3302 

118.39 

2.07330 

0.00845 

7 

.3665 

•I343I 

.10549 

93.88 

1.97259 

.01065 

8 

.3264 

.10651 

.08366 

74-45 

.87189 

•01343 

9 

.2906 

.08447 

.06634 

59-04 

.77118 

.01694 

10 

.2588 

.06699 

.05261 

46.82 

•67047 

.02136 

11 

0.2305 

0.05312 

0.04172 

37-13 

1.56977 

0.02693 

12 

•2053 

.04213 

•03309 

29-45 

.46906 

•03396 

J3 

.1828 

•03341 

.02624 

23-35 

•36835 

.04282 

14 

.1628 

.02649 

.O2O8I 

18.52 

.26764 

.05400 

15 

.1450 

.02101 

.01650 

14.69 

.16694 

.06809 

16 

17 

0.12908 
•II495 

0.016663 
.013214 

0.013087 
.010378 

11.648 
9-237 

1.06623 
0.96552 

0.0859 
.1083 

18 

.10237 

.010479 

.008231 

7-325 

.86482 

•!365 

!9 

.09116 

.008330 

.006527 

5-809 

.7641  1 

.1721 

20 

.08118 

.006591 

.005176 

4.607 

.66340 

.2171 

21 

0.07229 

O.OO5227 

0.004105 

3-653 

0.56270 

0.2737 

22 

.06438 

.004145 

•003255 

2.898 

.46199 

•345° 

23 

•05733 

.003287 

.002582 

2.298 

.36128 

•4352 

24 

.05106 

.002607 

.OO2O47 

1.822 

.26057 

.5488 

2S 

•04545 

.002067 

.001624 

1-445 

•15987 

.6920 

26 

0.04049 

0.0016394 

0.0012876 

I-I459 

0-05916 

0.873 

27 

.03606 

.OOI3OOI 

.OOIO2II 

.9088 

^95845 

I.IOO 

28 

.03211 

.0010310 

.0008098 

.7207 

•85775 

1.388 

29 

.02859 

.0008176 

.OOO6422 

•5715 

•75704 

1.750 

30 

.02546 

.0006484 

.0005093 

•4532 

-65633 

2.206 

31 

O.O2268 

0.0005142 

O.OOO4O39 

0-3594 

^55562 

2.782 

32 

.02019 

.0004078 

.0003203 

.2850 

.45492 

3-508 

33 

.01798 

.0003234 

.0002540 

.2261 

•35421 

4.424 

34 

.Ol6oi 

.0002565 

.OOO2OI4 

•1793 

•25350 

5-578 

35 

.01426 

.0002034 

.0001597 

.1422 

.15280 

7-034 

36 

0.01270 

O.OOOl6l3 

0.0001267 

0.1127 

1.05209 

8.87 

3Z 

.01131 

.OOOI279 

.OOOIOO5 

.0894 

2.95138 

II.I8 

38 

39 

.OIOO7 
.00897 

.0001014 
.0000804 

.OOOO797 
.0000632 

.0709 
.0562 

.85068 
-74997 

14.10 

17.78 

40 

.00799 

.0000638 

.0000501 

.0446 

.64926 

22.43 

SMITHSONIAN  TABLES. 


60 


TABLE  66. 


CONSTANTS   OF   COPPER   WIRE. 

.according  to  the  American  Brown  and  Sharp  Gauge.     Metric  Measure.    Temperature  o°  C.     Density  8.90. 

Electrical  Constants. 


Resistance  and  Conductivity. 

Gauge 
Number. 

Ohms 
Metre. 

Log. 

Metres 
per 
Ohm. 

Ohms 
per 
Gramme. 

Grammes 
Ohm. 

0.0001519 

4.18150 

6584. 

o.ooooooi  592 

6283000. 

OOOO 

.0001915 

.28221 

5221. 

.OOOOOO253I 

3951000. 

OOO 

.0002415 

.38191 

4141. 

.OOOOOO4O24 

2485000. 

oo 

.0003045 

.48362 

3284. 

.0000006398 

1  563000. 

o 

0.0003840 

4.58433 

2604. 

O.OOOOOIOI7 

982900. 

1 

.0004842 

.68503 

2065. 

.OOOOOl6l8 

618200. 

2 

.0006106 

•78574 

1638. 

.000002572 

388800. 

3 

.0007699 

.88645 

1299. 

.000004090 

244500. 

4 

.0009709 

•98715 

1030. 

.000006504 

153800. 

5 

O.OOI224 

3.08786 

816.9 

0.00001034 

96700. 

6 

.001  544 
.001947 

.18857 
.28928 

647-8 
5I3-7 

.00001644 
.00002615 

60820. 
38250. 

8 

.002455 

.38998 

407.4 

.00004157 

24050. 

9 

•003095 

.49069 

323.I 

.00006610 

15130. 

10 

0.003903 

3.59140 

256.2 

O.OOOIO5II 

95*4- 

11 

.004922 

.69210 

203.2 

.00016712 

5984. 

12 

.006206 

.79281 

161.1 

.00026574 

3763. 

13 

—  -  .007826 

•89352 

127.8 

.00042254 

2367. 

14 

.009868 

•99423 

101.3 

.00067187 

1488. 

13 

0.01244 
.01569 

2.09493 
.19564 

80.37 
63-73 

0.0010683 
.0016987 

936.1 

588.7 

16 
17 

.01979 
.02495 

•29635 
•397°5 

5°-54 
40.08 

.OO27OIO 
.0042948 

370.2 
232.8 

18 
19 

.03146 

•49776 

31-79 

.0068290 

146.4 

20 

0.03967 

2.59847 

25.21 

0.010859 

92.09 

21 

.05002 

.69917 

19.99 

.017266 

57-92 

22 

.06308 

.79988 

I5-85 

.027454 

36.42 

23 

•07954 
.10030 

_-90059 
1.00130 

12.57 
9-97 

.043653 
.069411 

22.91 
11.88 

24 

25 

0.12647 

T.I  0200 

7-907 

O.IIO37 

9.060 

£      O 

26 

.15948 

.20271 

6.270 

•17549 

5.698 

27 

.201  10 

.30342 

4-973 

.27904 

3.584 

28 

•25358 

.40412 

3-943 

.44369 

2.254 

29 

.31976 

.50483 

3.127 

•70550 

1.417 

3° 

0.4032 
.CO84 

7.60554 

.70624 

2.480 
1.967 

1.1218 

1-7837 

0.8914 

.5606 

31 

32 

•  JX-^T' 

.6411 

.8085 

.80695 

.90766 

1.560 
1-237 

2.8362 
4.5097 

•3526 
.2217 

33 

34 

1.0194 

0.00837 

0.981 

7.1708 

•1394 

35 

1.2855 
I.62IO 
2.0440 
2.5775 
3.250I 

0.10907 

.20978 
.31049 
.41119 
.51190 

07779 
.6169 
.4892 
.3880 
.3076 

11.376 

18.130 

28.828 

45-838 
72.885 

0.08790 

.055*6 
.03469 
.02182 
.01372 

36 

P 

39 
40 

SMITHSONIAN  TABLES. 


61 


TABLE  67. 


SIZE,  WEIGHT,  AND    ELECTRICAL 

Size,  Weight,  and  Electrical  Constants  of  pure  hard  drawn  Copper  Wire  of  different  numbers. 
Size  and  Weight. 


Gauge 
Number. 

Diameter 
in  Inches. 

Square  of 
Diameter 
(Circular 
Inches). 

Section 
in  Sq.  Inches. 

Pounds 
per  Foot. 

Log. 

Feet 

per  Pound. 

7-0 

0.500 

0.2500 

0.1963 

0.75760 

T.87944 

I.320 

6-0 

.464 

•2153 

1691 

.65243 

•81453 

I-583 

5-0 

0.432 

0.1866 

0.1466 

0.56554 

1.75247 

1.768 

4-0 

.400 

.1600 

•1257 

.48466 

.68562 

2.062 

3~° 

•372 

.1384 

.1087 

.41936 

.62258 

2-385 

2-0 

•348 

.1211 

.0951 

•36699 

.56466 

2725 

o 

.324 

.1050 

.0825 

.31812 

•50259 

3-M3 

1 

0.300 

C.O9OOO 

0.07069 

0.27274 

T.43574 

3.667 

2 

.276 

.07618 

.05983 

.23084 

.36332 

4.332 

3 

.252 

.06350 

.04980 

.19244 

.28430 

5.196 

4 

.232 

.05382 

.04-7 

.16310 

.21246 

6.131 

5 

.212 

.04494 

•0353° 

.13620 

•i34'7 

7-342 

6 

0.192 

0.03686 

0.02895 

o.  1  1  1  7  1 

1.04810 

8.95 

7 

.176 

.03098 

•02433 

.09387 

2.97252 

10.65 

8 

.160 

.02560 

.O2OIO 

•077  58 

.88974 

12.89 

9 

,'  -144 

.02074 

.01629 

.06284 

.79^22 

'5-91 

10 

.128 

.01638 

.01287 

.04965 

.69592 

20.14 

11 

0.116 

0.013456 

0.010568 

0.04078 

2.61041 

24-52 

12 

.104 

.010816 

.008495 

.03278 

•5I557 

30-51 

J3 

.092 

.008464 

.006648 

.02565 

.40907 

38.99 

14 

.080 

.006400 

.005027 

.01939 

.28768 

51-56 

75 

.072 

.005184 

.00407  1 

.01571 

.19616 

63.66 

16 

0.064 

0.004096 

0.003217 

0.012412 

2.09386 

80.6 

1? 

.056 

.003  1  36 

.002463 

.009503 

3-97/87 

105.2 

18 

.048 

.002304 

.COlSlO 

.006982 

.84398 

143.2 

*9 

.040 

.001600 

.001257 

.004649 

.68502 

200.2 

20 

.036 

.001296 

.OOIOl8 

.003927 

.59410 

254.6 

21 

0.032 

0.0010240 

0.0008042 

0.003103 

3.491-0 

322.3 

22 

.028 

.0007840 

.0006157 

.002376 

.37581 

420.9 

23 

.024 

.0005760 

.0004524 

.001746 

.24192 

572.9 

24 

.022 

.0004840 

.0003801 

.001467 

.16634 

681.8 

25 

.020 

.0004000 

.0003141 

.001212 

.08356 

824.9 

25 

o.orSo 

0.0003240 

0.0002545 

0.0009818 

4.99209 

1018. 

27 

.or  64 

.000  ."630 

.OOO2  I  I  2 

.0008  1  5  1 

.91119 

1227. 

28 

.0148 

.0002190 

.000  1  7  28 

.0006638 

.82202 

1506. 

29 

.0136 

.0001850 

.000  1  4  S3 

.0005605 

.74858 

1784. 

30 

.0124 

.0001538 

.0001208 

.0004660 

.66834 

2146. 

31 

0.0116 

0.00013156 

0.00010568 

0.0004078 

4.61041 

2452. 

32 

.0108 

.0001  1664 

.00009161 

•0003535 

.54835 

2829. 

33 

.0100 

.00010000 

.00007854 

.0003030 

.48150 

3300. 

34 

.0092 

.00008464 

.00006648 

.000256=; 

.40907 

3899. 

35 

.0084 

.00007056 

.00005542 

.0002  1  38 

.33006 

4677. 

36 

0.0076 

0.00005776 

0.00004  s  36 

0.0001750 

4-24313 

57i3. 

37 

.0068 

.00004624 

.00003632 

.0001404 

•14752 

7120. 

38 

.0060 

.00003600 

.00002827 

.0001091 

.03780 

9167. 

39 

.0052 

.00002704 

.00002  i  24 

.0000819 

SWS1 

I  2  2OO. 

40 

.0048 

.00002304 

.00001810 

.0000682 

.84398 

14660. 

41 

0.0044 

0.00001036 

0.00001521 

0.00005867 

5.76840 

17050. 

42 

.0040 

.00001600 

.00001257 

.00004849 

.68562 

2O62O. 

43 

.0036 

.00001296 

.00001018 

.00003927 

.59410 

25460. 

44 

.0032 

.00001024 

.00000804 

.00003103 

.49180 

32230. 

45 

.0028 

.00000784 

.00000616 

.00002381 

.37681 

41990. 

46 

0.0024 

0.00000576 

0.00000452 

0.00001746 

5.24192 

57290. 

47 

.0020 

.00000400 

.00000314 

.OOOOI2I2 

.08356 

82490. 

'   4» 

.0016 

.00000256 

.00000201 

.00000776 

6.88974 

128900. 

49 

.0012 

.00000  i  44 

.OOOOOII3 

.OOOOO436 

.63986 

2292OO. 

50 

.0010 

.00000  1  oo 

.OOOOOO79 

.OOOOO3O3 

.48150 

330000. 

SMITHSONIAN   TABLES. 


62 


CONSTANTS   OF   COPPER   WIRE. 

according  to  the  British  Standard  Wire  Gauge.     British  Measure.    Temperature  o°  C.     Density  8.90. 

Electrical  Constants. 


TABLE  67. 


Resistance  and  Conductivity. 

Gauge 
Number. 

Ohms  per  Foot. 

Log. 

Feet  per  Ohm. 

Ohms  per  Pound. 

Pounds  per  Ohm. 

0.00003918 

5-59310 

25520. 

0.000051719 

I9335- 

7-o 

.00004550 

.65799 

21980. 

.000069736 

14339- 

6-0 

0.00005249 

5.72006 

19050. 

0.00009281 

10775- 

5-0 

.OOOO6I22 

.78691 

16330. 

.00012627 

7920. 

4-0 

.00007078 

.84994 

14130. 

.00016880 

5924- 

3-° 

.00008089 

.90787 

12360. 

.00022040 

4537- 

2-O 

.00009331 

•96994 

10720. 

.00029333 

3409- 

O 

O.OOOIO88 

4.03679 

9188. 

0.0003991 

2505.8 

1 

.OOOI286 

.10921 

7777- 

.0005570 

1795.2 

2 

.0001543 

.18823 

6483. 

.0008015 

1247.7 

3 

.OOOI82O 

.26005 

5495- 

.0011158 

896.2 

4 

.0002180 

•33836 

4588. 

.0016002 

624.2 

5 

0.0002657 

4-42443 

3763- 

0.0023786 

420.4 

6 

.0003162 

.50000 

3162. 

.0033688 

296.9 

7 

.0003826 

.58279 

2613. 

.0049323 

202.7 

8 

.0004724 

.67430 

2117. 

.0075176 

I33-° 

9 

.0005979 

.77661 

1673- 

.0084978 

117.7 

10 

0.0007280 
.0009056 

4.86211 
•95696 

1373-6 
1104.2 

0.017853 
.027631 

56-013 
36.191 

11 

12 

.0011573 

3-06345 

864.1 

.045121 

22.163 

13 

.0015305 

.18485 

653-4 

.078927 

12.669 

14 

.0018896 

•27636 

529.2 

.I2O282 

8.314 

15 

0.002391 

3-37867 

418.1 

0.19267 

5.1902 

16 

.003124 

•49465 

320.2 

.32868 

3-0423 

17 

.004252 
.0061  22 

.62855 
.78691 

235-2 

.60893 
1.26268 

1.6423 
0.7919 

18 
19 

.007558 

.87842 

I32-3 

1.92451 

.5196 

20 

0.00957 

3-98073 

104.54 

3.0827 

0-32439 

21 

.01249 

2.0967  1 

80.04 

5-2599 

.19011 

22 

.OI7OI 

.23061 

58.80 

9.7429 

.10264 

23 

.O2O24 

.30618 

49.41 

13.7988 

.07246 

24 

.02506 

.38897 

20.2028 

.04951 

25 

0.03023 

2.48048 

33-o8 

30.792 

0.032478 

26 

.03642 

.56134 

27.46 

56.254 

.017778 

27 

.04472 
.05296 

.65051 
.72395 

22.36 

18.88 

67.373 
94.488 

.014843 
.010583 

28 

29 

.06371 

.80419 

I5-70 

136.724 

.007314 

3° 

0.07449 

2.87211 

13.42 

182.68 

0.005474 

31 

.08398 

.92418 

11.91 

237-59 

.004209 

32 

.09796 

.99103 

IO.2I 

323.25 

.003094 

33 

.11573 

1.06345 

8.64 

451.21 

.002216 

34 

.13883 

.14247 

7.20 

649.25 

.001540 

35 

0.16959 

7.22940 

5-897 

968.9 

O.OOIO72I 

ff 

36 

.21184 

.32601 

4720  . 

1508.3 

.0006630 

37 

.272IO 
.36226 
•42515 

•43473 
.55902 
.62855 

3-675 
2.760 
2.352 

2494.2 
4421.0 
6089.3 

.0004009 
.OOO2262 
.0001642 

39 
40 

0.5060 

7.70412 

1.976 

8624. 

o.ooo  1  1  596 

41 

.6122 

•755s 

.78691 
.87842 

•633 
-323 

12627. 
19245. 

.00007919 
.00005196 

42 
43 

.9566 
1.2494 

-98073 
0.0967  1 

•045 
0.800 

30827. 
52468. 

.00003244 
.00001906 

44 
45 

1.7006 
2.  CO  CO 

0.23061 
.38897 

0.5880 
-3991 

97429. 
2O2O28. 

0.000010264 
.000004950 

46 

47 

3&&I 

6.8025 
9.7956 

•3    si 

.58279 
.83267 
.99103 

*^^ 

.2613 
.1470 

.1021 

493232.     4 

1558851. 

3232451- 

.000002027 
.000000642 
.000000196 

48 
49 
50 

SMITHSONIAN  TABLES. 


TABLE  68. 


SIZE,   WEIGHT,    AND    ELECTRICAL 

Size,  Weight,  and  Electrical  Constants  of  pure  hard  drawn  Copper  Wire  of  different  numbers 
Size  and  Weight. 


Gauge 
Number. 

Diameter  in 
Centimetres. 

Square  of 
Diameter 
(Circular 
Cms.). 

Section  in 
Sq.  Cn,s. 

Grammes 
per  Metre. 

Log. 

Metres 
per  Gramme,      i 

7-0 

1.2700 

1.6129 

1.267 

1127.4 

3.05209 

0.000887 

6-0 

.1786 

.3890 

.091 

970.9 

2.98719 

.001032 

5-° 

1-0973 

1.2040 

0.9456 

841.6 

2.92512 

O.OOII88 

4-0 

.0160 

.0323 

.8107 

721.6 

•85827 

.001386 

0.9449 

0.8928 

.7012 

624.1 

•79524 

.OOIOO2 

2-0 

.8839 

•7815 

.6136 

546.3 

•73741 

.001831 

0 

.8230 

.6773 

•53r9 

484.4 

.68524 

.002064 

1 

2 

0.7620 
.7010 

0.58065 

•49!57 

ie 

405.9 

343-6 

2.60839 
.53607 

0.002464 
.002910 

3 

4 

.6401 
•5893 

.40970 

.3218 
.2727 

286.4 
242.7 

•4^5 
.38|I2 

•003492 
.004120 

5 

.5385 

.28996 

.2277 

202.7 

.30682 

.004934 

6 

0.4877 

0.23783 

0.18679 

166.25 

2.22075 

0.000015 

8 

•4470 
.4064 

•'9984 
.16516 

.15696 

•I2973 

139.69 
"5-45 

.06239 

.007159 
.008662 

9 

10 

.3658 
.3251 

•13378 
.10570 

.10507 
.08302 

73-^9 

1.97087 
.86857 

.010694 

•OI3533 

11 

0.2946 

0.08681 

0.06818 

60.68 

1.78307 

0.01648 

12 

.2642 

.06978 

.05480 

48.78 

.68822 

.02051 

13 

•2337 

•05461 

.04289 

38-17 

.58172 

.02620 

14 

'5 

.2032 
.1829 

.04129 
•03344 

•03243 
.02627 

28.86 
23-38 

$3? 

•03465 
.04278 

16 

0.16256 

0.026426 

0.020755 

18.514 

1.26751 

0.05401 

17 

.14224 

.020233 

.015890 

14.142 

.15053 

.07071 

18 

.12192 

.014865 

.011675 

10.390 

.01663 

.09625 

19 

.10100 

.010323 

.008107 

7.216 

0.85827 

•13858 

20 

.09144 

.008361 

.006567 

5-845 

.76675 

.17109 

21 

0.08128 

0.006606 

0.005188 

4.618 

0.66445 

0.2165 

22 

.07  1  1  2 

.005058 

.003972 

3-536 

.54847 

.2828 

23 

.06096 

.003716 

.002922 

2.598 

.41457 

•3850 

24 

.05588 

•003123 

.002452 

2.183 

.33899 

.4581 

25 

.05080 

.002581 

.002027 

1.804 

.25621 

•5544 

26 

0.04572 

0.0020903 

0.0016417 

1.4625 

0.16509 

0.6838 

27 

.04166 

.0017352 

.0013628 

.2129 

.08384 

.8245 

28 

•03759 

.    .0014132 

.0011099 

0.9878 

1.99467 

1.0123 

29 

•03454 

.0011922 

.0009363 

•8333 

.92083 

.2000 

30 

•03150 

.0009920 

.0007791 

•6§34 

.84099 

4422 

31 

0.02946 

0.0008681 

0.0006818 

0.6068 

1.78307 

1.648 

32 

.02743 

.0007525 

.0005910 

.5260 

.72100 

I.90I 

33 

.02540 

.0006452 

.0005067 

.4510 

.65415 

2.217 

34 

•02337 

.0005461 

.0004289 

•3817 

.58172 

2.620 

35 

•02134 

.0004552 

•0003575 

.3182 

.50271 

3-143 

36 

O.OI93O 

0.0003726 

0.0002927 

0.2605 

1.41578 

3.839 

37 

.01727 

.0002983 

.0002343 

.2090 

.31917 

4.784 

38 

•01524 

.0002323 

.0001824 

.1623 

.21045 

6.l6o 

39 

.OI32I 

.0001746 

.0001370 

.1219 

.08616 

8.201 

40 

.OI2I9 

.0001486 

.0001  167 

.1039 

.01663 

9.625 

41 

0.01118 

0.0001249 

0.0000982 

0.0873 

2.94105 

11.45 

42 

.01016 

.0001032 

.0000813 

.0722 

.85827 

13.86 

43 

44 

.00914 

.00813 

.0000836 
.0000661 

.0000656 
.0000519 

.0584 
.0462 

•76675 
.66445 

17.11 

21.65 

45 

.007  1  1 

.0000506 

.0000397 

•°354 

•54847 

28.28 

46 

0.00610 

0.00003716 

0.0000292 

0.0260 

2.41457 

38.5 

47 

.00508 

.00002581 

.0000203 

.0180 

.2S62I 

48 

.00406 

.00001652 

.0000129 

.0115 

•06239 

86.6 

49 

.00305 

.00000929 

.0000073 

.0065 

3.8l25I 

154.0 

50 

.00254 

.00000645 

.0000051 

•0045 

•65415 

221.8 

SMITHSONIAN  TABLES. 


64 


CONSTANTS    OF    COPPER    WIRE. 

according  to  the  British  Standard  Wire  Gauge.     Metric  Measure.     Temperature  o°  C.     Density  8.90. 

Electrical  Constants. 


TABLE  68, 


Resistance  and  Conductivity. 

Gauge 
Number. 

Ohms  per  Metre. 

Log. 

Metres  per  Ohm. 

Ohms  per  Gramme. 

Grammes  per  Ohm. 

O.OOOI286 

4.10907 

7779- 

0.0000001140 

8770000. 

7-0 

.0001493 

.17398 

6699. 

.0000001537 

6504000. 

6-0 

0.0001722 

4.23605 

5814. 

0.0000002046 

4887000. 

5-° 

.OOO2OO9 

.30289 

4979- 

.0000002784 

3592000. 

4-0 

.0002322 

•36593 

4306. 

.0000003721 

2687000. 

.0002653 
.0003061 

.42376 
.48592 

3769. 
3266. 

.0000004857 
.0000006319 

2059000. 
1583000. 

2-O 
0 

0.0003571 

4-55277 

2801. 

0.0000008798 

II37OOO. 

1 

.0004218 

.62510 

2371- 

.0000012275 

814700. 

2 

.0005061 

.70421 

1976. 

.0000017671 

565900. 

3 

.0005971 

.77604 

1675- 

.0000024600 

406500. 

4 

.0007151 

•85434 

1398. 

.0000035279 

283500. 

5 

0.0008718 

4.94041 

1147.1 

0.000005244 

190700. 

6 

.0010375 

3.01599 

963.9 

.000009350 

IO7OOO. 

7 

.0012554 

.09877 

796.6 

.000010874 

91960. 

8 

.0015499 

.19029 

645.2 

.000016573 

60340. 

9 

.0019615 

.29259 

509.8 

.000026547 

37670. 

10 

0.002388 

3-378IO 

418.7 

0.00003936 

25410. 

11 

.002978 
.003796 
.005022 

•47295 

•57934 
•70083 

335-8 
263.4 
199.1 

.00006092 
.00009945 
.00017398 

16420. 
10060. 

5748. 

12 
13 
14 

.006199 

•79235 

161.3 

.00026518 

3771- 

15 

0.007846 

3.89465 

127.45 

0.0004238 

2359-6 

16 

.010248 

2.01064 

97.58 

.0007246 

1380.1 

n 

.013949 

•14453 

71.69 

.0013425 

744-9 

18 

.020086 

.30289 

49-79 

.0027837 

359-2 

19 

.024798 

•39441 

40.32 

.0042428 

235-7 

20 

0.03138 

2.49671 

31.86 

0.005398 

185.25 

21 

.04099 

.61270 

24-39 

•OII594 

86.25 

22 

•74659 

17.92 

.021479 

46.56 

23 

.06640 

.82217 

15.06 

.030421 

32.87 

24 

.08034 

.90495 

12.45 

•044539 

22.45 

25 

0.09919 

2.99647 

IO.O&2 

0.06782 

14-745 

26 

.11949 
.14672 

1.07733 
.16649 

8.369 

6.8  1  6 

.09851 
.14853 

10.151 
6.732 

2 

•I739I 

.24034 

5-750 

.20869 

4.792 

29 

.20901 

.32017 

4.784 

.30142 

3-3J8 

3° 

0.2388 

1.37810 

4.187 

0.3936 

2.5407 

31 

•2755 

.44017 

3.629 

•5238 

1.9091 

32 

.3214 

.50701 

3.112 

.7126 

1-4033 

33 

•3797 
•4555 

^65846 

2.634 
2.196 

•9947 

I-43I3 

1-0053 
0.6987 

34 
35 

0.5564 

174539 

1-7973 

2.136 

0.46816 

36 

.6950 

.84200 

4388 

3-333 

.30003 

37 

.8927 

.95070 

.1202 

7.019 

.14247 

38 

1.1885 

0.07501 

0.8414 

9-747 

.10260 

39 

•3949 

.14453 

.7169 

13-424 

.07449 

40 

i.  660 

0.2201  1 

O.6O24 

19.01 

0.05260 

41 

2.009 

.30289 

•4979 

27.84 

.03592 

42 

2.480 

•39441 
.49671 

•4033 
.3186 

42.43 
67.96 

•02357 
.01471 

43 
44 

4.099 

.61270 

.2440 

"5-94 

.00863 

45 

5-579 

0.74659 

0.1792 

210.4 

0.004753 

46 

8.034 

.90495 

.1245 

445-4 

.002245 

47 

12.554 

1.09877 

.0797 

1087.4 

.000920 

48 

22.318 

•34865 

.0448 

34367 

.000291 

49 

32-138 

.50701 

.0311 

7126.3 

.000140 

50 

SMITHSONIAN  TABLCS. 


TABLE  69. 


SIZE,  WEIGHT,  AND    ELECTRICAL 

Size,  Weight,  and  Electrical  Constants  of  pure  hard  drawn  Copper  Wire  of  different  numbers 
Size  and  Weight. 


Gauge 
Number. 

Diameter 
in  Inches. 

Square  of 
Diameter 
(Circular 
Inches). 

Sections  in 
Sq.  Inches. 

Pounds 
Foot. 

Log. 

Feet 
per 
Pound. 

[  OOOO 
000 

0.454 
•425 

0.206  1 
.1806 

0.16188 

.14186 

0.6246 

•5474 

1.79561 

.73828 

1.601 

1.827 

00 

.380 

.1440 

.11341 

•4376 

.64107 

2.285 

0 

•340 

.1156 

.09079 

•35°3 

.54446 

2.855 

1 

2 

0.300 
.284 

0.09000 
.08065 

0.07069 
•06335 

0.2727 
.2444 

7-43574 
.38814 

3.666 
4.091 

3 

•259 

.06708 

.05269 

•2033 

.30810 

4.919 

4 

•238 

.05664 

.04449 

.1717 

.23465 

5.826 

5 

.220 

.04840 

.03801 

.1467 

.16634 

6.818 

6 

O.2O1 

0.04I2I 

0.03237 

0.12488 

1.09649 

8.008 

9 

.180 

3 

.03240 
.02723 
.02190 

•02543 
.02138 
.01720 

.09818 
.08250 
.06638 

2.99204 
.91647 
.82202 

10.185 

12.121 
1  5.065 

10 

•134 

.01796 

.OI4IO 

.05441 

•73571 

18.379 

11 

O.I  2O 

O.OI4400 

O.OII3IO 

0.04364 

2.63986 

22.91 

12 

.109 

.OIl88l 

.009331 

.03600 

'55635 

27.77 

13 

•095 

.009025 

.007088 

•02735 

.43695 

36.56 

14 

.083 

.006889 

.005411 

.02088 

•31965 

47-90 

15 

.072 

.005184 

.004072 

.01571 

.19616 

63.65 

16 

0.065 

0.004225 

0.0033183 

0.012803 

2.10733 

78.10 

17 

.058 

.003364 

.0026421 

.010194 

•00835 

98.10 

18 

.049 

.002401 

.0018857 

.007276 

3.86189 

137-44 

J9 

.042 

.001764 

.0013854 

.005346 

.72800 

187.06 

20 

•035 

.OOI225 

.0009621 

.003712 

.56963 

269.40 

21 

0.032 

O.OOIO24 

0.0008042 

0.003103 

3.49180 

322.3 

22 

.028 

.000784 

.0006158 

.002376 

•37581 

420.9 

23 

.025 

.000625 

.0004909 

.001894 

.27738 

528.0 

24 

.022 

.000484 

.0003801 

.001467 

.16634 

681.8 

25 

.O2O 

.OOO4OO 

.0003142 

.OOI  21  2 

.08356 

824.9 

26 

O.OlS 

0.000324 

0.0002545 

0.0009818 

4.99204 

1018. 

27 

.Ol6 

.000256 

.OOO20  1  1 

.0007758 

.88974 

1289. 

28 

.014 

.000196 

.0001539 

.0005940 

•77375 

1684. 

29 

.013 

.000169 

.0001327 

.OOO5I2I 

.70939 

1953- 

3° 

.OI2 

.000144 

.0001131 

.0004364 

.63986 

2292. 

31 

0.010 

O.OOOIOO 

0.00007854 

0.00030304 

4.48150 

3300. 

32 

.009 

.000081 

.00006362 

.00024546 

.38998 

4074. 

33 

.008 

.000064 

.00005027 

.00019395 

.28768 

5*56- 

34 

.007 

.000049 

.00003848 

.00014849 

.17169 

6734- 

35 

.005 

.000025 

.00001963 

.00007576 

5-87944 

13200. 

36 

0.004 

0.000016 

0.00001257 

0.00004849 

5.68562 

20620. 

SMITHSONIAN  TABLES. 


66 


TABLE  69. 


CONSTANTS   OF   COPPER   WIRE. 

according  to  the  Birmingham  Wire  Gauge.     British  Measure.    Temperature  o°  C.    Density  8.90. 

Electrical  Constants. 


Resistance  and  Conductivity. 

Gauge 
Number. 

Ohms 
per 
Foot. 

Log. 

Feet 
Ohm. 

Ohms 
per 
Pound. 

Pounds 
per 
Ohm. 

0.00004752 

5.67692 

21040. 

0.0000761 

13140. 

OOOO 

.00005423 
.00006784 

•73425 
.83146 

18440. 
14740. 

.0000991 
.0001550 

10090. 
6451. 

000 
00 

.00008474 

.92807 

IlSoo. 

.0002419 

4I34. 

O 

0.0001088 
.OOOI2I4 

4'03679 
.08439 

9188. 
8234. 

0.0003991 
.0004969 

2505-8 
2012.5 

1 

2 

.0001460 

.16443 

6848. 

.0007183 

1392.2 

3 

.0001729 

.23788 

5783. 

.0010074 

992.6 

4 

.OOO2O24 

.30618 

4941. 

.0013799 

.724.7 

5 

0.0002377 
.0003023 

4.37604 
.48048 

4207. 
3308. 

0.001903 
.003079 

525.26 
324.76 

6 

7 

.0003598 

.55606 

2779. 

.004361 

229.30 

8 

.0004472 

•65051 

2236. 

.006737 

148.43 

9 

.0005455 

.73682 

I833- 

.OIOO25 

99-75 

10 

O.OOO68O2 

4.83267 

1470.2 

0.01559 

64.148 

11 

.0008245 

.91618 

1212.9 

.02290 

43.670 

12 

.0010854 

3-03558 

921.3 

.03969 

25-i95 

*3 

.0014219 

.15287 

703-3 

.o68ll 

14.002 

J4 

.0018896 

.27636 

529.2 

.12028 

8.314 

15 

0.002318 

3-36520 

43I-3 

O.lSlI 

5-5225 

16 

.002980 
.004080 

47417 
.61064 

335-6 
245.1 

357 

3.4211 
1-7835 

17 

18 

•005553 
.007996 

•74453 
.90289 

180.1 
125.1 

1.0388 
2.I54I 

0.9627 
•4643 

19 

20 

0.009566 
.012494 
.015709 
.020239 
.024489 

3-98073 
2.09671 

'I9S1S 

.30618 
.38897 

104.54 
80.04 
63.66 
49.41 
40.83 

3-083 

5-259 
8.275 

13-799 
20.203 

0-32439 
.19015 
.12085 
.07246 
.04950 

21 

22 
23 
24 

25 

0.02887 
.03826 
.04998 
.05796 
.06802 

5.46048 
.58279 
.69877 

•763I4 
.83266 

34.64 
26.13 

20.01 

I7-25 
14.70 

29.41 
49-32 
84.14 
113.18 
155.88 

0.034006 
.020275 
.011885 
.008835 
.006415 

26 

3 

29 
30 

0.09796 
.12095 

•15306 
.19991 
.39182 

2.99103 
1.08254 
.18485 
.30083 
•59309 

10.209 
8.269 

6-533 
5.002 

2-552 

323.2 
492.7 
789.2 
1346.3 

5J7i-9 

0.0030936 
.0020290 
.0012671 
.0007420 
.0001933 

31 

32 
33 
34 
'35 

O.6I222 

1.78691 

1.663 

12627. 

0.00007920 

36 

SMITHSONIAN  TABLES. 


TABLE  7O. 


SIZE,  WEIGHT,  AND    ELECTRICAL 

Size,  Weight,  and  Electrical  Constants  of  pure  hard  drawn  Copper  Wire  of  different  numbers 
Size  and  Weight. 


Gauge 
Number. 

Diameter  in 
Centimetres. 

Square  of 
Diameter 
(Circular 
Cms.). 

Section  in 
Sq.  Cms. 

Grammes 
Metre. 

Log. 

Metres 
per 
Gramme. 

0000 

I.I532 

1.3298 

1.0444 

929.5 

2.96826 

0.001076 

000 
OO 

•0795 
0.9652 

•1653 
0.9316 

.9152 
•7317 

814.6 
651.2 

.91093 
.81372 

.OOI228 
.001536 

O 

.8636 

.7458 

.5858 

52L3 

.71711 

.001918 

1 

0.7620 

0.5806 

0.4560 

405.9 

2.60839 

0.002464 

2 

.7214 

.5216 

.4087 

3637 

.56079 

.002749 

3 

•6579 

.4328 

•3399 

302-5 

.48075 

.003306 

4 

5 

.6045 

.5588 

.3655 
.3123 

.2870 
.2452 

2554 
218.3 

.40730 
.33899 

•003915 
.004581 

6 

0.5I56 

0.2659 

0.20881 

185.84 

2.26914 

0.005381 

7 

.4572 

.2090 

.16417 

146.11 

.16469 

.006844 

8 

.4191 

.1756 

•'3795 

122.78 

.08912 

.008145 

9 

•3759 

•1413 

.11099 

98.78 

1.99467 

.010124 

10 

.3404 

.1158 

.09098 

80.98 

.90836 

.012349 

11 

0.3048 

0.09290 

0.07297 

64.94 

1.81251 

0.01540 

12 

.2769 

.07665 

.06160 

54.83 

.73900 

.01824 

13 

.2413 

.05823 

•04573 

40.70 

.60960 

.02457 

H 

.2108 

.04445 

•03491 

31.07 

•49231 

.03219 

15 

.1829 

•03345 

.02627 

23-43 

.36981 

.04268 

16 

0.16510 

0.027258 

0-021409 

19.054 

1.27998 

0.05248 

17 

.I4732 

.021703 

.017046 

i5-J7i 

.18101 

.06^92 

18 

.12446 

.015490 

.012166 

10.828 

•03454 

.09235 

19 

.10668 

.011381 

.008938 

7-955 

0.90065 

.12571 

20 

.08890 

.007903 

.006207 

5-524. 

.74229 

.18103 

21 

0.08128 

0.006606 

0.005189 

4.618 

0.66445 

0.2165 

22 

.07112 

.005058 

•003973 

3-536 

•54847 

.2828 

23 

.06350 

.004032 

.003167 

2.820* 

•45°°3 

-3547 

24 

.05588 

•003123 

.002452 

2.183 

•33899 

.458  r 

25 

.05080 

.002581 

.002027 

1.804 

.25621 

•5544 

26 

0.04572 

0.0020903 

0.0016418 

1.4611 

0.16469 

0.6^44 

27 

.04064 

.0016516 

.0012972 

•T545 

.06239 

.8662 

28 

•03556 

.0012645 

.0009932 

0.8839 

1.94641 

«-*3*3 

29 

.03302 

.0010903 

.0008563 

.7621 

.88204 

.3122 

30 

.03048 

.0009290 

.0007297 

.6494 

.81251 

•5399 

31 

0.02540 

0.0006452 

0.0005067 

0.4510 

1.65415 

2.217 

32 

.02286 

.0005226 

.0004104 

•3653 

.56263 

2-738 

33 

.02032 

.0004129 

.0003243 

.2886 

•46033 

3-465 

34 

.01778 

.0003161 

.0002483 

.2210 

•34435 

4-525 

35 

.01270 

.0001613 

.0001267 

.1127 

.05209 

8.870 

36 

0.01016 

O.OOOIO32 

0.0000811 

0.0722 

2.85827 

13.861 

SMITHSONIAN  TABLES. 


68 


TABLE  70, 


CONSTANTS   OF   COPPER   WIRE. 

according  to  the  Birmingham  Wire  Gauge.     Metric  Measure.    Temperature  o°  C.     Density  8.90. 

Electrical  Constants. 


Resistance  and  Conductivity. 

Gauge 
Number. 

Ohms 
Metre. 

Log. 

Metres 
Ohm. 

Ohms 
per 
Gramme. 

Grammes 
Ohm. 

0.0001559 
.0001779 

4.19290 

.25024 

6414. 
5620. 

0.0000001677 
.0000002184 

5962000. 
4578000. 

0000 
000 

.OOO2226 

•34745 

4493- 

.0000003418 

2926000. 

oo 

.0002780 

.44406 

3597. 

.0000005333 

1875000. 

o 

0.0003571 

4-55277 

2800. 

0.0000008798 

II37OOO. 

1 

.0003985 
.0004791 

.60038 
.68041 

2510. 

2087. 

.0000010955 
.0000015837 

912800. 
631400. 

2 

3 

.0005674 
.0006640 

•75386    . 
.82217 

1763. 

1506. 

.OOOOO222IO 
.0000030420 

450200. 
328700. 

4 
5 

0.0007799 

4.89202 

1282.2 

0.000004196 

238300. 

6 

.0009257 
.0011804 
.0014672 

.99647 
3.07205 
.16649 

1080.3 

847.2 
681.6 

.000006789 
.000009615 
.000014853 

147300. 
IO4OOO. 
67330. 

9 

.0017898 

.25280 

558.7 

.OOOO22IO3 

45240. 

10 

0.002232 
.002643 

3-34865 
.42216 

448.1 

378.3 

0.00003437 
.00004822 

29100. 
20740. 

11 

12 

.003561 

•55*57 

280.8 

.00008749 

11430. 

13 

.004665 

.66886 

214.4 

.00015016 

6660. 

14 

.006185 

.79135 

161.7 

.00026396 

3789. 

15 

0.007607 
.009553 

•OI3385 

3.88119 
.98016 
2.12662 

131.46 
104.68 
74.71 

0.0003992 
.0006297 
.0012362 

2504.9 
1588.0 
808.9 

16 

17 
18 

.018219 

.26052 

54.89 

.0022902 

436.6 

J9 

.026235 

.41888 

38.12 

.0047489 

2IO.6 

20 

0.03138 
.04099 
.05142 

2.49671 
.61270 
•7IH3 

31.86 

24-39 
19.45 

0.006796 
.011594 
.018243 

147.14 
86.25 

54.82 

21 

22 
23 

.06640 

.82217 

15.06 

.030421 

32.87 

24 

.08034 

.90495 

12.45 

•044539 

22.45 

25 

0.09919 
•  12583 
.16397 
.19016 

.22138 

2.99647 
1.09877 
.21476 

•27913 
•34865 

1  0.08 

7-947 
6.099 

5-259 
4-5r7 

0.06789 
.10874 

•1855° 
.24951 

•34367 

J4-731 
9.196 

5-39J 
4.008 
2.910 

26 

27 
28 
29 
30 

0.3214 
.3968 

1.50701 

3.112 
2.520 
1.991 

0.7126 
1.0862 
1.7398 

1.4032 
0.9206 

•5748 

31 

32 
33 

A  r  rn 

8168^ 

2.9861 

•3349 

34 

•°559 

1.2855 

0.10907 

0-778 

11.4020 

.0877 

35 

2.0086 

0.30289 

0.498 

27.8370 

0-0359 

36 

SMITHSONIAN  TABLES. 


69 


TABLE  71. 


STRENGTH    OF    MATERIALS, 


(a)     METALS. 

Name  of  metal. 

Tensile  strength  in 
pounds  per  sq.  in. 

3OOOO-4OOOO 
50000-150000 
IIOOOO-I4OOOO 
950OO-II5OOO 
OOOOO-7OOCO 
38000-41000 
13000-29000 
8OOOO-I  2OOOO 
5OOOO-6OOOO 
2600-3300 
3QOOO 
5OOOO 
42OOO 
100000-200000 
I  50000-33000 
4OOO-5OOO 
7000-13000 
22000-30000 

Brass  wire,  hard  drawn  
Bronze,  phosphor,  hard  drawn         .         .         .        *        . 

"        silicon           "         "     .         .         .         .         .        .         . 

Copper  wire,  hard  drawn          J        .     '   » 

"          "     annealed       
Ldad,  cast  or  drawn         
Palladium  t      

Platinum  t  wire        ........... 

Silver  t  wire    .         .                                   ...                 ... 

"      hard       "          "       
Tin,  cast  or  drawn  .                         ........ 

Zinc,  cast          ............ 

"     drawn     ............ 

(6)     STONES   AND    BRICKS. 

Name  of  substance. 

Resistance  to  crush- 
ing in  pounds 
per  sq.  in. 

Basalt       .... 

I8OOO-27OOO 
300-1  500 
1500-5000 
9OOO-26OOO 
I7OOO-26OOO 
4000-9000 
9OOO-22OOO 
4500-8000 
IIOOO-30000 

Brick  soft                                                  N  .         .        .   •     •        •        .         . 

"      hard       

Marble     .                  .                  

Slate         

(c-)     TIMBER. 

Tensile  strength           Resistance  to 
Name  of  wood.                                                             in  pounds  per               crushing  in 
sq.  in.                pounds  persq.  in. 

>            6000-9000 
9OOO-IOOOO 
5000-7000 
4000-6000 
6OOO-IOOOO 

7OOO-I2OOO 
6000-8000 

7OOO-IOOOO 
5000-7000 
4000-6000 
6000-9000 
5000-8000 
4000-8000 

Beech         .        .        .         iiooo-iSooc 

Mulberry   8000-14000 

Walnut      ....                                                                8000  14000 

?  strength  of  most  materials  is  so  variable  that  very  little  is  gained  by  simple  tabulation  of  the  results  which 
have  been  obtained.  A  few  approximate  results  are  given  for  materials  of  common  occurrence,  mainly  to  indicate  the 
limits  between  which  the  strength  of  fairly  good  specimens  may  lie.  Some  tables  are  also  given  indicating  the  rela- 
tion of  strength  to  composition  in  the  case  of  alloys.  It  has  not  been  thought  worth  while  to  state  these  results 
in  other  than  the  ordinary  inch  pound  units. 

t  On  the  authority  of  Wertheim. 

$  The  crushing  strength  of  cast  iron  is  from  5.5  to  6.5  times  the  tensile  strength. 

NOTES.  —  According  to  Boys,  quartz  fibres  have  a  tensile  strength  of  between  1 16000  and  167000  pounds  per  square 
inch. 

Leather  belting  of  single  thickness  bears  from  400  to  1600  pounds  per  inch  of  its  breadth. 
SMITHSONIAN  TABLES.  ~ 


PHYSICAL    PROPERTIES   OF   STEEL.* 


TABLE  72, 


Percentages  of 



xi 

gg 

a 

3 

1 

J3 

Is 

I*1' 

S 

'~  8 

1 

1 

|| 

11 

ft 

S. 

P. 

Si. 

C. 

Mn. 

Cu. 

Co. 

Ni. 

Sb. 

fi 

f  8 

'tti 

£.£ 

c  o- 

.£•= 

ft 

ii 

•S   i 

3    , 

•«  c 

'<?.  c 

§ 

C/3  a 

" 

>• 

«§. 

«.£ 

W 

.004 

.014 

.145 

•257 

.O2O 

.002 

.008 

.OIO 

216 

379 

246 

9-S 

1  06 

3°-9 

.009 
.Oil 

.084 
.109 

.163 
.168 

.009 
.042 

.O2O 
.051 

.023 
.028 

.021 

.028 

.016 

.044 

252 
276 

434 
481 

260 

234 

I2.3 

17.4 

I29 
IIP 

32-6 

27-5 

.027 

.247 

.216 

.036 

.072 

.027 

.048 

.070 

322 

S29 

243 

24.7 

117 

24.9 

.014 

.029 

•037 

.161 

.121 

.OOI 

trace 

trace 

317 

534 

277 

18.4 

'51 

32.0 

trace 
.008 
.056 

•039 
•034 

.084 

•073 
.007 

•139 

.OOO 
.064 
.165 

.014 

.008 
•364 

.036 
.016 
.076 

•057 
.023 
.107 

.115 

260 
419 

478 

605 
649 

687 

2|0 
263 
26l 

I5.6 
37-9 

IIO 

130 

IIO 

20.8 

22.3 

18.1 

.004 

.024 

.087 

•447 

.072 

.005 

.018 

.023 

46l 

7SS 

271 

46.0 

124 

18.6 

.058 

.128 

.013 

•254 

•341 

.278 

•045 

.065 

487 

785 

293 

55-o 

91 

15-5 

.066 

.099 

.016 

.326 

•525 

.306 

•054 

.078 

549 

793 

255 

58.0 

38 

5.6 

.002 

.022 

.123 

•595 

.J24 

.001 

.007 

.006 

480 

828 

42.7 

21.0 

.008 

.062 

.071 

•447 

•493 

.007 

.040 

.065 

484 

859 

284 

38.2 

174 

22-7 

.041 
.062 

:!# 

.028 
.018 

•355 
•390 

.404 
.584 

•253 

•344 

•049 

•073 

.102 

.no 

543 
565 

880 
953 

254 
259 

55-9 
73-7 

49 

44 

6.7 

5-6 

.002 

.002 

.020 
.026 

.096 
.164 

.652 
•935 

.061 
.099 

.030 
.004 

.007 
.018 

.018 
.016 

SS7 

955 
9S7 

269 
278 

50.2 
6S-3 

112 
123 

HI 

•043 

.104 

.074 

•756 

•465 

•346 

.OS2 

.120 

652 

IOIO 

237 

94.6 

14 

i  j 

.028 

.005 

.028 

.690 

•459 

.022 

.OOO 

.coo 

Si6 

IO22 

285 

SS-6 

37 

4.6 

.003 

.031 

.204 

•929 

.129 

.007 

.013 

.OIO 

590 

1050 

284 

62.1 

148 

16.0 

.038 

.092 

.070 

•387 

.625 

.210 

•050 

•ri5 

631 

III2 

279 

83.2 

«3S 

13-7 

.OOI 

.015 

.150 

.971 

.074 

.003 

.003 

.015 

555 

II7I 

262 

65.6 

99 

9.9 

.000 

.019 

.192 

1.105 

.226 

.OOI 

.OO2 

.004 

668 

I2S4 

272 

82.7 

93 

9.0 

.014 

.063 

•043 

.681 

•625 

.038 

.000 

.000 

614 

1288 

260 

82.2 

108 

9-9 

STEEL  CONTAINING  CHROMIUM. 

trace 

.O2O 

.116 

.461 

.027 

trace 

.000 

.612  Cr. 

370 

810 

27  S 

28.3 

IIO 

iS-6 

1    .OOI 

.019 

.136 

•454 

.023 

.000 

.000 

.921  Cr. 

49  S 

9iS 

287 

44.8 

157 

19.1 

trace 

.007 

.154 

•639 

.050 

.008 

trace 

1.044  Cr. 

Soo 

967 

281 

56.1 

-5 

3-5 

— 

— 

.000 

— 

— 

— 

2.200  Cr. 

675 

1030 

— 

— 

19.9 

~ 

I.IOO 

~ 

~ 

4.000  Cr. 

1770 

1778 

~ 

~ 

2 

7-5 

STEEL  CONTAINING  TUNGSTEN. 

__ 



.09 

1.99 

.10 

7.81  per  cent  tungsten    . 



1464 







o.o 

— 

— 

•OS 

2.06 

2.66 

6.73    "      " 

— 

700 

— 

— 

— 

o.o 

Same  after  heating  to  dull  red  and  quenching  in  oil 

— 

940 

— 

— 

— 

o.o 

~ 

.21 

1.20 

•35 

6.45  per  cent  tungsten    . 

1900 

0.75 

STEEL  CONTAINING  MANGANESE. 

.06 

.08 

•37 

•72 

9.8 

(  one  test    . 
(  another  tes 

— 

1065 
1190 

— 

— 

— 

22.0 
28.9 

,t  .     .     .     . 

*  The  samples  here  given  are  arranged  in  the  order  of  ultimate  strength.  The  table  illustrates  the  great  com- 
plexity of  the  problem  of  determining  the  effect  of  any  given  substance  on  the  physical  properties.  It  will  be  noticed 
that  the  specimens  containing  moderately  large  amounts  of  copper  are  low  in  ductility,  — that  high  carbon  or  high  sum 
of  carbon  and  manganese  generally  gives  high  strength.  The  first  specimen  seems  to  indicate  a  weakening  effect 
of  silicon  when  a  moderate  amount  of  carbon  is  present.  It  has  to  be  remembered  that  no  table  of  this  kind  proves 
much  unless  nearly  the  same  amount  of  work  has  been  spent  on  the  different  specimens  in  the  process  of  manufacture. 
Most  of  the  lines  give  averages  of  a  number  of  tests  of  similar  steels.  The  table  has  been  largely  compiled  from  the 
Report  of  the  Board  on  Testing  Iron  and  Steel,  Washington,  1881,  and  from  results  quoted  in  Howe  s  Metallurgy 
of  Steel." 

t  The  strengths  and  elasticity  data  here  given  refer  to  bar  or  plate  of  moderate  thickness,  and  are  in  pounds  per 
square  inch.  Mild  steel  wire  generally  ranges  in  strength  between  100000  and  200000  pounds  per  square  inch,  with 
an  elongation  of  from  8  to  4  per  cent.  Thoroughly  annealed  wire  does  not  differ  greatly  in  strength  from  the  data 
given  in  the  table  unless  it  has  been  subjected  to  special  treatment  for  the  purpose  of  producing  high  density  and 
fine-grained  structure.  Drawing  or  stretching  and  subsequent  rest  tend  to  increase  the  Young  s  Modulus. 


TABLE  73. 


ELASTICITY    AND   STRENGTH    OF    IRON.* 


Area  of  cross  sec- 

tion of  the  bar  in 
percentage  of  the 
area  of  the  cross 
section  of  the 

Relative  values  of 
ultimate  strength. 

Relative  values  of 
the  stress  at  the 
yield  point. 

pile. 

I 

125 

194 

2 

112 

170 

3 
4 

1  06 
104 

I44 
140 

The  variation  of  the  yield  point  is  not 
regular,  and  seems  to  have  been  much 

5 
7 

103 
IOI 

130 
114 

affected  by  the  temperature  of  rolling. 

10 

100 

IOO 

15 

98 

92 

TABLE  74. 

APPROXIMATE    VARIATION    OF   THE    STRENGTH    OF    BAR    IRON,   WITH 
VARIATION    OF   SECTION. t 


Diameter 
in  inches. 

Strength  per  sq. 
in.  in  pounds. 

Total  strength  of 
bar. 

Diameter 
in  inches. 

Strength  per  sq. 
in.  in  pounds. 

Total  strength 
of  bar. 

2.2 

59000 

224000 

I.I 

543°° 

52OOO 

2.1 

585°° 

203000 

I.O 

54000 

42000 

2.0 

58000 

I82OOO 

0.9 

53700 

34000 

•9 

57600 

163000 

0.8 

53300 

27000 

.8 

57100 

145000 

0.7 

53000 

2OOOO 

•7 

56700 

I  29000 

0.6 

52700 

I4QOO 

.6 

56300 

113000 

o-5 

52400 

10300 

•5 

559oo 

99000 

0.4 

52100 

6600 

•4 

555oo 

85000 

0.3. 

51900 

3700 

•3 

55^00 

73000 

0.2 

51600 

1600 

.2 

547oo 

62OOO 

O.I 

5  'y» 

4OO 

*  This  table  was  computed  from  the  results  published  in  the  Report  of  the  U.  S.  Board  on  Testing  Iron  and  Steel, 
Washington,  1881,  and  shows  approximately  the  relative  effect  of  different  amounts  of  reduction  of  section  from  the 
pile  to  the  rolled  bar.  A  reduction  of  the  pile  to  10  per  cent  of  its  original  volume  is  taken  as  giving  a  strength  of 
loo,  and  the  others  are  expressed  in  the  same  units. 

t  The  strength  of  bar  iron  may  be  taken  as  ranging  from  15  per  cent  above  to  15  per  cent  below  the  numbers  here 
given,  which  represent  the  average  of  a  large  number  of  tests  taken  from  various  sources. 

NOTES.  — The  stress  at  the  yield  point  averages  about  60  per  cent  of  the  ultimate  strength,  and  generally  lies  be- 
tween 50  and  70  per  cent.  The  variation  depends  largely  on  the  temperature  of  rolling  if  the  iron  be  otherwise  fairly 
pure. 

According  to  the  experiments  of  the  U.  S.  Board  for  Testing  Iron  and  Steel,  above  referred  to,  a  bar  of  iron  which 
has  been  subject  to  tensile  stress  up  to  its  limit  of  strength  gains  from  10  to  20  per  cent  in  strength  if  allowed  to  rest 
free  from  stress  for  eight  days  or  more  before  breaking.  The  effect  of  stretching  and  subsequent  rest  in  raising  the 
elastic  limit  and  tensile  strength  was  discovered  by  Wohler,  and  has  been  investigated  by  Bauschinger,  who  shows 
that  the  modulus  of  elasticity  is  also  raised  after  rest.  The  strengthening  effect  of  stretching  with  rest,  or  continuous 
very  slowly  increased  loading,  has  been  rediscovered  by  a  number  of  experimenters. 

SMITHSONIAN  TABLES. 

72 


TABLES  75-77. 

EFFECT  OF  RELATIVE  COMPOSITION  ON  THE   STRENGTH  OF  ALLOYS 
OF   COPPER,  TIN,  AND    ZINC.* 


TABLE  75.  —  Copper-Tin  Alloys.    (Bronzes.) 


TABLE  76.  —  Copper-Zinc  Alloys.    (Brasses. 


.c 

*o 

•« 

§ 

&  . 

|| 

-a  a 

Sol 

4/55 

bC  ^ 

II 

c 

£& 

5* 

f  ! 

IF 

Is 

£ 

Pounds  per  square  inch. 

I"3 

I8 

100 

OO 

28000 

14000 

42000 

8. 

44 

95 

5 

31000 

17000 

46000 

10. 

4i 

90 

IO 

29000 

2IOOO 

54000 

4- 

31 

85 

15 

33000 

26OOO 

74000 

1.6 

24 

80 

20 

32000 

28OOO 

i  24000 

°-5 

H 

75 

25 

ISOOO 

ISOOO 

i  50000 

o.o 

8 

70 

30 

6500 

6500 

143000 

0.0 

2 

65 

35 

2800 

2800 

75000 

o.o 

4 

J3 

•H-  . 

MtC 

0 

"5 

J>  M 

.SS. 

.£ 

It 

1 

c:  • 

s  e 

ttj  *-• 

H 

T3  C 

p 

ii 

a* 

rt 

HR 

g.s 

8  o 

04 

OH 

Pounds  per  square  inch. 

£w 

100 

0 

27000 

14000 

41000 

7 

95 

5 

28000 

I2OOO 

28000 

12 

90 

10 

3OOOO 

IOOOO 

29000 

18 

J5 

15 

32OOO 

9000 

33000 

25 

80 

20 

34000 

8000 

39000 

33 

75 

25 

37000 

9000 

46000 

P 

70 

30 

4IOOO 

IOOOO 

54000 

38 

65 

35 

46000 

13000 

63000 

33 

60 

40 

49000 

17000 

74000 

*9 

55 

45 

44000 

2OOOO 

90000 

IO 

5° 

So 

3OOOO 

2400O 

116000 

4 

45 

55 

I4OOO 

I4OOO 

126000 

o 

TABLE  77.  -  Copper-Zinc-Tin  Alloys.§ 


Percentage  of 

Tensile 

Percentage  of 

Tensile 

strength 

strength 

in  pounds 

in  pounds 

Copper. 

Zinc. 

Tin. 

per  sq.  in. 

Copper. 

Zinc. 

Tin. 

per  sq.  in. 

45 

50 

5 

15000 

[25 

5 

45000 

50 

45 

5 

5OOOO 

20 

10 

44000 

5° 

40 

10 

15000 

70 

1   I5 

15 

37000 

[43 

2 

65000 

10 

20 

30000 

1  40 

5 

62OOO 

1    5 

25 

24000 

55 

35 

IO 

32500 

20 

5 

45000 

30 
[37 

15 

3 

15000 
6OOOO 

75 

J'5 
lio 

IO 

15 

45000 
43000 

fin 

J35 

5 

52500 

I   5 

20 

4IOOO 

130 

IO 

4OOOO 

('5 

5 

45000 

[20 

20 

IOOOO 

80 

]io 

IO 

45000 

3° 

5 

50000 

(    5 

15 

475°° 

25 

IO 

42000 

8s 

10 

5 

43  5°° 

65 

•<  20 

15 

30000 

°j 

\    5 

IO 

46500 

15 

20 

1  8000 

90 

5 

5 

42000 

IO 

25 

I2OOO 

*  These  tables  were  compiled  from  the  results  published  by  the  U.  S.  Board  on  Testing  of  Metals.  The  numbers, 
refer  to  unwrought  castings,  and  are  subject  to  large  variations  for  individual  specimens. 

t  The  crushing  strengths  here  given  correspond  to  10  per  cent  compression  for  those  cases  where  the  total  com- 
pression exceeds  that  amount. 

t  For  crushing  strength,  10  per  cent  compression  was  taken  as  standard. 

§  This  table  covers  the  range  of  triple  combinations  of  these  three  metals  which  contain  alloys  of  useful  strength 
and  moderate  ductility.  The  weaker  cases  here  given,  and  those  lying  outside  the  range  here  taken,  are  generally  weak 
and  brittle.  The  absolute  strength  may  of  course  be  varied  by  the  method  of  fusing  and  casting,  and  certainly  can  be 
greatly  increased  by  working.  The  object  of  the  table  is  to  show  relative  values,  and  to  give  an  idea  of  the  strength  of 
sound  castings  of  these  alloys. 


SMITHSONIAN  TABLES. 


73 


TABLE  78. 


ELASTIC   MODULI, 

Rigidity  Modulus.* 


_____  —  
Substance. 

Modulus  of  Rigidity. 

Authority. 

Pounds  per 
square  inch 

-7-   I06. 

Grammes  per 
square  centi- 
metre -~  10°. 

Metals  :  — 

Aluminium 
Brass  and  Bronze  wire 

3.4-4.8 
4.6-5.8 

32O-4IO 

Thomson!-Katzenelsohn. 
Various. 

Copper,  drawn    .        ,        . 

5-6-6.7 

5-° 

393-473 
352 

Thomson.! 
Katzenelsohn. 

German  silver 

6.2 

432 

" 

"           "... 

7-1 

496 

Gray. 

Gold,  pure  .... 

5.6 

395 

Katzenelsohn. 

"".... 

4.0 

281 

Thomson.! 

Iron,  soft     .... 

9.6 

671 

Wertheim. 

"     drawn         . 

10-14 

700-800 

Various. 

Platinum     .... 

8.9 

622 

Thomson.! 

"            • 

94 

663 

Pisati. 

Silver  .        .        .        .        v 

3-8 

270 

Thomson.! 

« 

3-6 
3-8 

aj 

Pisati. 
Baumeister. 

Steel,  cast   .        .        . 

10.6 

746 

Wertheim. 

"        "              .        . 

1  1.8 

829 

Pisati. 

Tin      

2.2 

Kiewiet. 

Zinc     

C.I 

360 

Thomson.! 

0 

54 

382 

Kiewiet. 

Glass         .'        .'        .'        '. 

Wertheim. 

ti 

-J.Q 

271 

Kowalski. 

Stone  :  — 

•j  y 

/  J 

Clay  rock    .        .     -V       . 

2-5 

177 

] 

Granite        .        .        .        .. 

1.8 

128 

Gray 

Marble         .... 

1.7 

119 

r  & 

Slate    

3-2 

229 

Milne. 

Tuff     

IO2 

j 

Wood       

.I-.I7 

7-12 

Gray. 

*  The  modulus  of  rigidity  as  used  in  this  table  may  be  shortly  defined  by  the  following  equation  :  — 

Modulus  of  rigidity  -  Intensity  of  tangential  stress. 
Distortion  in  radians. 

To  interpret  the  equation  imagine  a  cube  of  the  material,  to  four  consecutive  faces  of  which  a  tangential  stress  of 
uniform  intensity  is  applied,  the  direction  of  the  stress  being  opposite  on  adjacent  faces.  The  modulus  of  rigidity  is 
the  number  obtained  by  dividing  the  numerical  value  of  the  tangential  stress  per  unit  of  area  by  the  number  repre- 
senting the  change  of  the  angles  on  the  nonstressed  faces  of  the  cube  measured  in  radians, 
t  Lord  Kelvin. 


SMITHSONIAN  TABLES. 


74 


TABLE  79. 


ELASTIC  MODULI. 

Young's  Modulus.* 


Young's 

Modulus. 

Substance. 

Pounds  per 
square  inch 

-7-   I0». 

Grammes  per 
square  centi- 
metre -r  10°. 

Authority. 

Metals  :  — 
Brass  and  bronze,  cast  .... 

8.6-10 

14—17 

600-700 
IOOO—  I2OO 

Various. 

Copper,  drawn      

16-18 
15 

II50-I250 
1052 

« 
Wertheim. 

German  silver,  drawn  .... 

17-20 

12-14 

1209-1400 

8n-Q.So 

Various. 
« 

"      annealed      
Iron,  cast      ...... 
"      wrought        ..... 
Iron  wire       
Lead,  cast  or  drawn                       •. 
Palladium,  soft      
hard    

18 
8-i7t 
24-30 
«    « 

2.2-2.9 
14 
17 
27-26 

55* 
550-1200 
1700-2100 

156-200 

979 
1176 
1600-1700 

Wertheim. 
Various. 

Wertheim. 
u 

Various. 

"          soft        ....       •»•> 
Silver,  drawn         .         .         .               •  .  '" 
Steel      
"      hard  drawn  
Tin                                 .... 

22 
IO-IO-7 
23-30* 
27-30 

16 

!552 
700-750 
1600-2100 
1900-2100 
4*7 

Wertheim. 
Various. 

Various. 
Wertheim. 

12-14 

870-960 

Various. 

2.3 

160 

_ 

2.2-3.6 

151-255 

Beetz. 

Glass 

8.6-11.4 

600-800 

Various. 

Ice      

7-10 

500-700 

Stone  :  — 

4-7 

329 

N 

c.q 

416 

Gray 

Marble                             .         . 

C.7 

400 

\     & 

Slate               

9.8 

686 

Milne. 

Tuff                        

2.7 

189 

Whalebone         abt. 

0.85 

I.O-2.2 

60 
70-154 

Various. 

*  The  Young's  Modulus  of  elasticity  is  used  in  connection  with  elongated  bars  or  wires  of  elastic  material.  It  is 
the  ratio  of  the  number  representing  the  longitudinal  stress  per  unit  of  area  of  transverse  section  to  the  number  rep- 
resenting the  elongation  per  unit  of  length  produced  by  the  stress,  or :  — 

,,    ,  ,  Intensity  of  longitudinal  stress. 

Young  s  Modulus  =      E)ongation  per  unit  length. 

In  the  case  of  an  isotropic  substance  the  Young's  Modulus  is  related  to  the  elasticity  of  form  (or  rigidity  modulus) 
and  the  elasticity  of  volume  (or  bulk  modulus)  in  the  manner  indicated  in  the  following  equation  :  — 


where  E  is  Young's  Modulus,  n  the  rigidity  modulus  and  k  the  bulk  modulus. 

The  bulk  modulus  is  the  ratio  of  the  number  expressing  the  intensity  of  a  uniform  normal  stress  applied  all  over 
the  bounding  surface  of  a  body  (solid,  liquid  or  gas)  to  the  number  expressing  the  change  of  volume,  per 
produced  by  the  stress. 

t  The  modulus  for  cast  iron  varies  greatly,  not  only  for  different  specimens,  but  in  the  same  specimen  for  different 
intensities  of  stress.     It  is  diminished  for  tension  stress  by  permanent  elongation. 

I  See  also  Table  72. 
SMITHSONIAN  TABLES. 

75 


TABLES  8O,  81 


ELASTIC   MODULI. 

TABLE  80. —Variation  of  the  Rigidity  of  Metals  with  Temperature.* 

The  modulus  of  rigidity  at  temperature  t  is  given  by  the  equation  nt  =  «0  ( i  -f  at  -f  ${*  -f  yP). 


Metal. 

"0 

a 

ft 

y 

Authority. 

Brass 

320  X  io6 

—  .000455 

—  .00000136 



K.  &L. 

265  X  io'! 

—  .002158 

—  .00000048 

—  .0000000032 

Pisati. 

Copper  . 

397  X  ioa 

—  .0027  1  6 

4-  .00000023 

—  .0000000047 

" 

« 

390  X  10^ 

—  .000572 

—  .00000028 

— 

K.  &  L. 

Iron 

694  X  io6 

—  .000483 

—  .00000012 

— 

" 

M 

811  X  io6 

—  .000206 

—  .00000019 

+  .00000000  1  1 

Pisati. 

Platinum  . 

663  X  io« 

—  .0001  1  1 

—  .00000050 

4-  .0000000008 

" 

Silver 

257  X  io6 

—  .000387 

—  .00000038 

—  .00000000  1  1 

M 

Steel 

829  X  ios 

—  .000187 

—  .00000059 

+  .0000000009 

TABLE  81.  —  Ratio  p  of  Transverse  Contraction  to  Longitudinal  Extension  under  Tensile  Stress 

(Poisson's  Ratio). 


Name  of  substance. 


Range  of  the 
value  of  p. 


Mean 
of  each 
range. 


Final 
mean. 


Authority. 


Brass 


Copper 
ii 

Iron 


Lead 
Steel,  hard 


0.340-0.500 


0.224-0.441 


0.250-0.420 
0.214-0.268 


soft 


0.293-0.295 
0.275-0.328 
0.266-0.303 


Zinc 

Ebonite 

Ivory       

Paraffin 

Cork 

Caoutchouc  (for  small  extensions) 

«  «                   i< 

Jelly 


0.180-0.230 


0.370-0.640 


0.469  ] 

0.420 

0.387 ' 

0.325 

0-315 

0.226 

0.348 
0.332 

0.310 

0.253 
0.304 
0.243 

0-375  N 
0.294  ) 

0.294  > 
0.296  ) 
0.304  ] 
0.306  I 
0-253  [ 
0-333  J 
0.205 

about 


0-5°5  I 
0.500  J 
0.500 


0-357 


0.340 

0.277 

0-375 
0.295 

0.299 

0.205 
0.389 
0.500 
0.500 
o.ooo 

0.502 
0.500 


Everett. 

Baumeister. 

Kirchhoff. 

Mallock. 

Wertheim. 

Littmann. 

Mallock. 

Thomson. 

Everett. 

Mallock. 

Baumeister. 

Littmann. 

Mallock. 

Kirchhoff. 

Okatow 

Schneebeli. 

Okatow. 

Schneebeli. 

Mallock. 

Goetz  &  Kurz. 

Mallock. 


j  Rontgen. 

I  Amagat. 

Maurer. 


Katzenelsohn  gives  the  following  values,  together  with  the  percentage  variation  5  between  o°  and  100°  C. 


Substance. 


Aluminium     . 

Brass 

German  silver 

Gold       . 

Iron 

Platinum 

Silver 


0.13 

0.42 

0-33 
0.17 
0.27 
0.16 
o-37 


15-7 
3-9 
3-4 
2-5 
3-7 
5-5 

12.2 


*  According  to  the  experiments  of  Kohlrausch  and  Loomis  (Pogg.  Ann.  vol.  141),  and  of  Pisati  (N.  Cim.  (3)  vols.  4, 5). 
SMITHSONIAN  TABLES. 

76 


TABLE  82. 
ELASTICITY   OF   CRYSTALS.* 


The  formulae  were  deduced  from  experiments  made  on  rectangular  prismatic  bars  cut  from  the  crystal.  These  bars 
were  subjected  to  cross  bending  and  twisting  and  ihe  corresponding  Elastic  Moduli  deduced.  The  symbols 
_  a  ..  _  0  ..  -..j  _  0  ..  .  ....  jJ?...: • r.L.  ,___.,_  ....  j  e  less  transverse 

for  extension  or 
aare  centimetre. 


were  suojectea  to  cross  bending  and  twisting  and  me  corresponding  t-lastic  Moduli  deduced 
a-  ft  y,  O-L  Pi  YI  and  o2  )32  y.z  represent  the  direction  cosines  of  the  length,  the  greater  and  th 
dimensions  of  the  prism  with  reference  to  the  principal  axis  of  the  crystal.  E  is  the  modulus 
compression,  and  T  is  the  modulus  for  torsional  rigidity.  The  moduli  are  in  grammes  per  square 


Barite. 

TO10 

-£-  =  16.130*+  i8.5i/3<4-  10.427*  + 2(38.79)8 VH  i5-2i7°«2  +8.88cTj32) 

TO10 

-      =  69.52^  +  1 17.66/3*  4-  1 16.467*  4-  2(20.16/8  V  +  85.297'V  +  1 27.35^) 


Beryl  (Emerald). 


E 

10 


=  4.325  sin'^4-  4-6i9cos404"  J3-328  sin2^cos2p 


—  -  =  1  5.00  —  3.67  5  cos402  —  1  7.536  coofy  cos'2<j>i 

Fluor  spar. 

^  =  13.05  -6.26  (a*  +)8»  +  74) 

I^  =  58.04  —  50.08  (j3  V2  +  7-a'2  +  «^2) 

Pyrites. 


^=18.60-17. 


Rock  salt. 

^-  =  33.48  —  9.66  (< 

^=154.58-77.28  (/3V  +  7-«- 

Sylvine. 


where  0  ^i  ^2  are  the  angles  which 
the  length,  breadth,  and  thickness 
of  the  specimen  make  with  the 
principal  axis  of  the  crystal. 


^-  =  306.0  —  192.8  (/8V  +  7-«2  4-  a2/3') 
Topaz. 

^°  =  4.341  a4  4-  3-460/3*  4-  3-7717*  +  2  (3.879/8  V  +  28.567^ 

-^°  =  I4.88a*  4-  I6-54/31 4-  16.457*  +  30-890V 
Quartz. 

E 

io10 


i^-  =  12.734  (i  — 72)24-  16.693  (I  —  72)72  +  9-7057*  —  8.460/87  (3a2  — , 


^-  =  19.665  +  9-o6o722  4-  22.9847 >i2  —  16.920  [(70  +  ^71)  (3001  —  000  — 


*  These  formulse  are  taken  from  Voigt's  papers  (Wied.  Ann.  vols.  31,  34,  and  35). 
SMITHSONIAN  TABLES. 

77 


TABLE  83. 


ELASTICITY   OF   CRYSTALS. 


Some  particular  values  of  the  Elastic  Moduli  are  here  given.  Under  E  are  given  moduli  for  extension  or  compression 
in  the  directions  indicated  by  the  subscripts  and  explained  in  the  notes,  and  under  T  the  moduli  for  torsional 
rigidities  round  the  axes  similarly  indicated. 


(a)  REGULAR  SYSTEM. 


Substance. 

Ea 

E6 

Ec 

Ta 

Authority. 

Fluor  spar      .     .     . 
Pyrites  

1473  X  io6 
-j  c  qo  X  i  o6 

1008  X  io6 
2^0  X  io6 

910  X  io6 
2310  X  io6 

345  X  io6 
1075  X  io6 

Voigt.t 

a 

Rock  salt  .... 
u 

Sylvine  

« 

416  X  io6 
403  X  io6 
401  X  io6 

772  X  IO6 

346  X  10° 
339  X  io6 
209  X  iob 
196  X  io6 

311  X  io6 

I29X  io6 
6cc  X  10° 

« 

Koch.J 
Voigt. 

Sodium  chloride 
Potash  alum  .     .     . 
Chrome  alum      .     . 
Iron  alum  .... 

405  X  io6 
181  X  io6 
161  X  lo*5 
186  X  io6 

319  X  io6 
199  X  io6 
177  X  io6 

— 

Koch. 
Beckenkamp.§ 

M 

(b)  RHOMBIC  SYSTEM. || 


Substance. 

EX 

E2 

E3 

E4 

E5 

E6 

Authority. 

Barite      . 
Topaz 

620  X  io6 
2304  X  io6 

540  X  io6 
2890  X  io6 

959  X  io6 
2652  X  io6 

376Xio« 
2670  X  io6 

702  X  io6 
2893  X  10° 

740  X  io6 
3180  X  io6 

Voigt. 

Substance. 

T12=T21 

T13  =  T31 

To  3  —  TS  2 

Authority. 

283  X  io6 

2Q7  X  IO6 

121  X  IO6 

Voigt. 

Topaz      

1  336  Xio6 

I  T  C  -3  X    I  O° 

1  1  04  X  i  o8 

In  the  MONOCLINIC  SYSTEM,  Coromilas  (Zeit.  fur  Kryst.  vol.  i)  gives 
Emax  =  887  X  io6  at  21.9°  to  the  principal  axis. 
Emin  =  313  X  io6  at  75.4°          "          "          " 
•\t-  )  Emu  =  2213  X  io6  in  the  principal  axis. 

Emin  =  1554  X  io6  at  45°  to  the  principal  axis. 


„ 


In  the  HEXAGONAL  SYSTEM,  Voigt  gives  measurements  on  a  beryl  crystal  (emerald). 
The  subscripts  indicate  inclination  in  degrees  of  the  axis  of  stress  to  the  principal  axis  of 
the  crystal. 

£0=2165X106,     E45=i796X  io6,    E90—  231 2  X  io6, 
TO  =  667  Xio6,      T.9o  =  883  Xio6.      The  smallest  cross   dimension   of  the 
prism  experimented  on  (see  Table  82),  was  in  the  principal  axis  for  this  last  case. 


In  the  RHOMBOHEDRIC  SYSTEM,  Voigt  has  measured  quartz.    The  subscripts  have  the 
same  meaning  as  in  the  hexagonal  system. 

£0=1030X106,     E_  45  =  1305X106,     £4.45  =  850X106,     £90  =  785X106, 

To  =  508  X  ro6,       T90  =  348  X  io6. 
Baumgarten  ^[  gives  for  calcspar 

£0=501X10^,     E_45  =  44i  Xio6,     E  +  45  =  772X106,     E90  =  79oXio6. 


*  In  this  system  the  subscript  a  indicates  that  compression  or  extension  takes  place  along  the  crystalline  axis,  and 
distortion  munrl  the  axis.    The  subscripts  b  and  c  correspond  to  directions  equally  inclined  to  two  and  normal  to  the 


third  and  equally  inclined  to  all  three  axes  respectively, 
t  Voigt,  "Wied.  Ann." 


vol.  31,  34-35. 

t  Koch,  "Wied.  Ann."  vol.  18. 
§  Beckenkamp,  "Zeit.  fur  Kryst."  vol.  io. 

||  The  subscripts  i,  2,  3  indicate  that  the  three  principal  axes  are  the  axes  of  stress  ;  4,  5,  6  that  the  axes  of  stress 
are  in  the  three  principal  planes  at  angles  of  45°  to  the  corresponding  axes. 
U  Baumgarten,  "  Pogg.  Ann."  vol.  152. 

SMITHSONIAN  TABLES. 

78 


TABLES  84-87. 


COMPRESSIBILITY  OF  CASES.* 


These  tables  give  the  relative  values  of  the  product  pv  for  different  pressures  and  temperatures,  and  hence  show  the 
departure  from  Boyle's  law.  The  pressures  are  in  metres  of  mercury,  or  in  atmospheres,  the  volume  being 
arbitrary.  The  temperatures  are  in  centigrade  degrees. 


TABLE  84.— Nitrogen. 


TABLE  85.  — Hydrogen. 


Pressure  in 

] 

values  of  pv  at  — 

metres  of 

mercury. 

i7°.7 

30°.  i 

5o°-4 

7S°-  S 

I00°.l 

30 

2745 

287  s 

3080 

3330 

3575 

60 

2740 

287  s 

3IOO 

3360 

3610 

IOO 

2790 

2930 

3170 

3445 

3695 

140 

2890 

3040 

3275 

355° 

3820 

1  80 

3OI5 

3T5° 

339° 

3675 

3950 

220 

3J4o 

3285 

3530 

3820 

4090 

260 

3290 

3440 

3085 

397  S 

4240 

300 

345° 

3600 

3840 

413° 

4400 

320 

3525 

3675 

39!.5 

4210 

4475 

Pressure  in 

Relative  values  of  pv  at  — 

metres  of 

mercury. 

i7°-7 

40°-4 

6o°.4 

8i°.i 

100°.  I 

30 

2830 

3045 

323  s 

343° 

3610 

60 

2885 

3110 

329S 

35oo 

3680 

IOO 

298S 

32OO 

3400 

3620 

3780 

140 

1  80 

3080 
3^5 

3300 
3420 

35°° 
3620 

3710 
3^30 

3880 

4010 

2  2O 

3290 

3S20 

3725 

3930 

4110 

260 

3400 

3625 

3*3° 

4040 

4220 

300 

3500 

3730 

3935 

4140 

4325 

320 

3550 

3780 

3990 

4200 

43*5 

TABLE  86.  — Methane. 


Pressure  in 

Relative  values  of  pv  at  — 

metres  of 

mercury. 

i4°-7 

29°-5 

40°.  6 

60°.  i 

79°.8 

I0o°.i 

3° 

2580 

2745 

2880 

3100 

_ 

_ 

60 

24OO 

2590 

2735 

2995 

3230 

3460 

IOO 

140 

2275 
22DO 

2480 
2480 

2640 

26SS 

2935 
2940 

3l8o 
3190 

3435 
3460 

180 

220 

2360 
2510 

2560 
2690 

2730 
2840 

3OI5 
3125 

3260 
3360 

3525 
3625 

TABLE  87.-Ethylene. 


Relative  values  of  pv  at  — 

metres  of 
mercury. 

i6°.3 

aoo. 

30°.  t 

4o°.o 

50°.  o 

6o°.o 

70°.  o 

79°-9 

89°.9 

I00°.0 

30 

1950 

2055 

222O 

2410 

2S80 

2715 

2865 

2970 

3090 

3225 

60 
90 
1  2O 

810 
1065 
1325 

900 
1370 

1190 

I  »95 

1440 

1535 
1540 

1875 
I5IO 
1660 

2IOO 
1710 
1780 

2310 

1930 

'95° 

2500 
2l6o 
2115 

2375 
2305 

2860 

2565 

2470 

150 
1  80 
2IO 

'59° 

i855 

2IIO 

1625 
1890 
2145 

1690 
22OO 

1785 
2035 
2285 

1880 
2130 

2375 

1990 

2225 
2470 

2125 
2340 
2570 

2250 
2450 
2680 

2390 

2565 
2790 

2540 
2700 

2910 

240 

270 

2360 
26lO 

2395 
264O 

2450 
2710 

2540 
2790 

2625 
2875 

2720 
2965 

2810 
3060 

2910 
3150 

3015 
3240 

3125 

3345 

300 
320 

2860 

3°35 

2890 
3^5 

2960 
3^5 

3040 
32OO 

3125 
3285 

3215 

3375 

3300 
3470 

3380 

3545 

347° 
3625 

r0 

*  Tables  84-89  are  from  the  experiments  of  Amagat;  "Ann.  de  chim.  et  de  phys.; 
p.  418. 
SMITHSONIAN  TABLES. 


1881,  or  "  Wied.  Bieb.,"  1881, 


TABLES  88-9O. 


COMPRESSIBILITY  OF  CASES. 

TABLE  88.  —  Carbon  Dioxide. 


Relative  values  of  pi>  at  — 

Pressure  in  '                                                    --- 

metres  of 
mercury. 

l3°.2 

35°-' 

40°.  2 

5o°.o 

6o°.o 

70°.  o 

8cr\0 

90°.  o 

IOO°.O 

I 

3° 

liquid 

2360 

2460 

2590 

2730 

2870 

2995 

3I2O  . 

3225 

5° 

- 

1725 

IQOO 

2145 

2330 

2525 

2685 

2845 

2980 

So 

625 

750 

825 

I2OO 

1650 

J975 

2225 

2440 

2635 

IIO 

825 

930 

980 

1090 

1275 

!55° 

1845 

2I05 

2325 

140 

IO2O 

1  1  2O 

"75 

1250 

1360 

1525 

.1715 

*95° 

2160 

170 

1210 

1310 

1360 

143° 

I520 

1645 

1780 

r975 

2135 

2CO 

1405 

I5OO 

!55° 

1615 

1705 

1810 

1930 

2075 

2215 

230 

I59° 

1690 

173° 

1800 

1890 

1990 

2O9O 

2210 

2340 

260 

1770 

1870 

1920 

1985 

2070 

2166 

226S 

2375 

2490 

290 

195° 

2O6O 

2100 

2170 

2260 

2340 

2440 

255° 

2655 

320 

2i35 

2240 

2280 

2360 

2440 

2525 

262O 

2725 

2830 

TABLE  89.  -  Carbon  Dioxide.* 


Value  of  the  ratio  pv  lfo\  at  — 

Pressure  in 

atmospheres. 

5°° 

100° 

200° 

250° 

0.725 

1.0037 

I.OO2I 

1  .0009 

1.0003 

1.440 

1.0075 

1.0048 

1.0025 

I.OOI5 

2.850 

1.1045 

1.0087 

I  .OO4O 

I.OO2O 

TABLE  90.  -  Air,  Oxygen,  and  Carbon  Monoxide  at  Temperature  between  18°  and  22°.t 

The  pressure^)  is  in  metres  of  mercury;  the  product  pv  is  simply  relative. 


Air. 

Oxygen. 

Carbon  monoxide. 

P 

pv 

P 

PV 

P 

PV 

2407 

26968 

24.07 

26843 

24.06 

27147 

34-90 

26908 

34-89 

26614 

34-91 

27102. 

45-24 

26791 

— 

45-25 

27007 

55-30 
64.00 

26780 
26778 

55-50 
64.07 

26185 
26050 

55-52 
64.00 

27025 

27060 

72.16 

26792 

72.15 

25858 

72.17 

27071 

84.22 

26840 

84.19 

25745 

84.21 

27158 

101.47 

27041 

101.46 

25639 

101.48 

24420 

1  33-89 

27608 

133-88 

2^671 

'339° 

28092 

177.60 
214.54 

28540 
29585 

1  77-58 
214.52 

25891 
26536 

1  77.6  r 

214.54 

29217 

30467 

250.18 

305/2 

250.18 

31722 

304.04 

32488 

303-03 

28756 

304-05 

33919 

*  Similar  experiments  made  on  air  showed  the  ratio  /z> 
t  Amagat,  "Compte  Rendu,"  1879. 

SMITHSONIAN   TABLES. 

80 


to  be  practically  constant. 


TABLES  91  ,  92, 

RELATION    BETWEEN    PRESSURE,   TEMPERATURE    AND 
VOLUME    OF    SULPHUR    DIOXIDE    AND    AMMONIA. 


TABLE  91.  — Sulphur  Dioxide. 

Original  volume  100000  under  one  atmosphere  of  pressure  and  the  temperature  of  the  experi- 
ments as  indicated  at  the  top  of  the  different  columns. 


c 

O)    W 
h    ^ 

«>  £ 

I5 

Corresponding  Volume  for  Ex- 
periments at  Temperature  — 

Volume. 

Pressure  in  Atmospheres  for 
Experiments  at  Temperature  — 

5S°.o 

99°.  6 

lS3°.2 

58°.o 

99°.6 

l83°.2 

IO 

8560 

9440 

_ 

12 

6360 

7800 

— 

1  0000 

— 

9.60 

— 

14 
16 
18 

4040 

6420 

53T° 
4405 

- 

9OOO 
8000 

9.60 
10.40 

10-35 
11.85 

_ 

20 

- 

4030 

- 

7000 

"•55 

I3-05 

- 

28 
32 

- 

3345 
2780 
2305 

3180 
2640 

6OOO 
5000 

12.30 
13-15 

14.70 
16.70 

~ 

36 

- 

1.935 

2260 

4000 

14.00 

20.15 

- 

40 

I 

- 

1450 

2040 
1640 

1375 

3500 
3000 

14.40 

23.00 
26.40 

29.10 

70 

— 

— 

1130 

2500 

- 

30.15 

33-25 

So 

— 

— 

93° 

2OOO 

_ 

35-20 

40.95 

9° 

IOO 

_ 

_ 

79° 
680 

1500 

- 

39.60 

55-2° 

1  20 

- 

- 

545 

IOOO 

- 

- 

76.00 

140 
1  60 

- 

- 

430 

325 

500 

•~ 

*• 

117.20 

TABLE  92. —Ammonia. 

Original  volume  100000  under  one  atmosphere  of  pressure  and  the  temperature  of  the  experiments  as 
indicated  at  the  top  of  the  different  columns. 


':          3 

i  § 

Corresponding  Volume  for  Ex- 
periments at  Temperature  — 

Volume. 

Pressure  in  Atmospheres  for  Experiments 
at  Temperature  — 

46°.6 

99  "'•6 

i83°.6 

30°.2 

46°.6 

99°.6 

i83°.o 

IO 

9500 

_ 

_ 

1  0000 

8.85 

9-5° 

_ 

12.5 

7635 

- 

9OOO 

9.60 

10.45 

- 

15 

20 

25 

SSSo 

63°5 
4645 
356° 

4875 
3835 

8000 
7OOO 

10.40 
11.05 

11.50 
13.00 

I2.OO 
13.60 

_ 

3° 

- 

2875 

3^5 

6000 

1  1.  80 

M-75 

15-55 

- 

35 
40 

45 
5° 

- 

2440 
2080 

1795 
1490 

2680 

2345 

2035 

1775 

5OOO 
4OOO 
35°° 

12.00 

1  6.60 

18-35 
18.30 

1  8.60 
22.70 
25.40 

19.50 
24.00 
27.20 

55 

- 

1250 

3000 

- 

- 

29.20 

3l-5° 

60 

- 

975 

145° 

2500 

- 

- 

34-25 

37-35 

70 
80 

"~ 

~ 

1245 
1125 

2000 

- 

- 

41.45 

45-50 

90 

_ 

- 

1035 

I5OO 

— 

— 

4970 

58.00 

IOO 

95° 

IOOO 

59.05 

93.60 

*  From  the  experiments  of  Roth,  "  Wied.  Ann."  vol. 
SMITHSONIAN  TABLES. 

81 


1880. 


TABLE  93. 


COMPRESSIBILITY    AND    BULK    MODULI    OF    LIQUIDS. 


Liquid. 

Temp. 

Cotrpression 
per  unit  vol- 
ume per  atmo. 
X  10". 

Pressure  or 
range  of  pres- 
sure in  at- 
mospheres. 

Authority. 

Calculated  values  of 
bulk  modulus  in  — 

Grammes 
per  sq.  cm. 

Pounds 
per  sq.  in. 

Acetone  .... 

14 

110 

f 

8-7-35-4 

Amagat    .... 

94  X  io5 

i.  34  Xi  o5 

Benzene   .... 

16 

90 

8.12-37.2 

"         .... 

115      " 

1.64      " 

15-4 

87.1 

1-4 

Pagliani  &  Palazzo 

119     « 

1.69      " 

'        .... 

50.1 

III     . 

1-4 

" 

93     " 

1.32      " 

Carbon  bisulphide 

O 

78 

Colladon  &  Sturm 

'33 

1.89      « 

'             ( 

15 

62.6 

— 

Quincke  .... 

165     " 

2-35    " 

'             ' 

I5.6 

87.2 

8-35 

Amagat    .... 

119     «« 

1.69    «• 

Chloroform 

IOO 

8.5 

174 
62.5 

1.267 

Grassi  

59 
165 

1.84    « 

M 

.J 

0.2 

62.6 

/ 
4.247 

a 

I6?      " 

2.1K      " 

H 

V 
12 

64.8 

^    **T"/ 

1.309 

« 

o 

2.26      " 

Ether  

1  1 

1  68 

8-30 

Amagat   .... 

61      " 

0.87       " 

u 

QQ 

8.6-13.5 

18.6  " 

O.26      " 

l( 

ss 

QQ 

C27 

86-16  c 

u 

19.8  " 

0.28      " 

u 

63 

J    J 

IOO 

u.v^—  jw.^ 

8.  C7-22.2Q 

« 

14-4   rt 

O.4Q      " 

H 

63 

O 
2Q1 

^'j/     m  "  ~:? 

8.0-14.11 

H 

O   r    T- 

xx  *fy 

O.5O            ' 

U 

o 

2C.4 

'yj 
IQO 

O/       O  r*  v)  J 

8.46—^4  22 

M 

CA   A      " 

O  77        ' 

Ethyl  alcohol    .    . 

*•  j-H- 
IO 

yw 
94-5 

^•^.\J     £O^*&* 

1-2 

Colladon  &  Sturm 

I09       « 

w./  / 

"          "         .     . 

12 

73-3 

1-456 

Tait     

140       " 

2.00       ' 

"          "         . 

14 

101 

8.5-37.12 

Amagat    .... 

102        " 

i-45     ' 

'          "         . 

28 

86 

150-200 

Barus        .... 

120       " 

1.71 

'          "         .     . 

28 

81 

1  50-400 

"           .... 

I27        « 

1.81      ' 

1          "         .     . 

65 

no 

1  50-200 

"           .... 

94 

i-34     ' 

'          "         . 

65 

IOO 

150-400 

"           .... 

103      ' 

1.47 

'          "         .     . 

IOO 

1  68 

150-200 

"           .... 

61      ' 

0.87      ' 

'          "         . 

IOO 

132 

150-400 

M 

78      ' 

i.  ii      ' 

<               u 

185 

320 

1  50-200 

u 

32 

0.46     ' 

'            "           .     . 

185 

274 

150-300 

"                  .... 

38 

0-54     ' 

'            "           . 

185 

245 

1  50-400 

"                 .... 

42 

0.60     ' 

"            "          . 

310 

4200 

1  50-200 

"                 .... 

2-5 

0.036  " 

«                      1C 

310 

2200 

150-300 

"                 .... 

4-7 

0.067  " 

"            "           .     . 

310 

I53° 

1  50-400 

"                 .... 

6.7 

0.095  " 

Ethyl  chloride  .     . 

12.8 

J56 

8-53~I3-9 

Amagat    .... 

66.3 

0.94 

"           "         . 

12.8 

8.53-36.45 

"           .... 

68.5 

o-97 

"           "         .     . 

61.5 

256 

12.65-34.36 

"           .... 

40-3 

0.57     " 

" 

99 

510 

12.79-19.63 

"           .... 

20.3 

0.29 

"           "         . 

99 

495 

12.79-34.47 

"           .... 

20.9 

0.30    " 

Glycerine      .    .     . 
Mercury  .... 

20.53 
o 

25-1 

3-38 

1-30- 

Quincke   .... 
Colladon  &  Sturm 

411.2 
3058.0 

5.85    « 
43-5 

"          .... 

o 

3-92 

Amagat    .... 

2629.0 

37-4 

Methyl  alcohol  .     . 

'3-5 

90.4 

I.OI2 

Grassi  

114.5 

1.63    ;• 

U                          « 

13.5 

QI  I 

7-5J3 

<* 

113.1 

1.61 

"        «     !  ! 

IOO 

y  A  •  * 
221 

8.68-37.32 

Amagat    .... 

046.3 

0.66    " 

Nitric  acid    .     .     . 

20.3 

338.5 

1-32 

Colladon  &  Sturm 

030.2 

°-43    " 

Oils  :  Almond  .     . 

— 

Quincke    .... 

187.7 

2.67     " 

Olive  .     .     . 

20.5 

— 

"          .... 

163.0 

2.32    « 

Paraffine 

14.84 

— 

De  Metz  .... 

164.5 

2-34    ' 

Petroleum  . 

16.5 

— 

Martini     .... 

148.3 

2.  II 

Rock  .     .     . 

19.4 

74.58 

— 

Quincke   .... 

138.4 

i-97     u 

Rape  seed   . 

20.3 

59.61 

— 

"          .... 

174-3 

2.48     « 

Turpentine  . 

19.7 

79.14 

— 

"          .... 

130.7  « 

1.86    " 

Sulphur  dioxide     . 

o 

3°2-5 

1-16 

Colladon  &  Sturm 

034-4  " 

0.49    " 

Toluene    .... 

IO 

79 

— 

De  Heen  .... 

130.7  " 

1.86    " 

Xylene     .... 

10 

73-8 

~ 

. 

140.0  " 

1.99    ' 

SMITHSONIAN  TABLES. 


82 


TABLE   93, 


COMPRESSIBILITY   AND    BULK   MODULI   OF   LIQUIDS, 


•^f— 

§  J  g 

i  A 

<U   O 

Calculated  values  of 

•ill 

SkS 

bulk  modulus  in  — 

Liquid. 

Temp. 

II        P 

Mn 

ilii 

Authority. 

Grammes 

Pounds 

<3£lx 

Hit  : 

per  sq.  cm. 

per  sq.  in. 

Water,  sea 

12 

44* 

, 

Tait      

234.8  X  lo5 

3-34  Xio5 

"        pure 

12 

47* 

I 

"        

22O.O      " 

3-i3    " 

<«           « 

O 

49-65 

1-24 

Colladon  &  Sturm     . 

208.0      " 

2.96    « 

« 

17.6 

42.9 

1-262 

Amagat    .   .—  .     .     . 

24I.I      " 

3-43    " 

a 

0 

50-3 

-5 

Pagliani  &  Vincentini 

206.0      " 

2-93    ' 

u 

10 

47.0 

-5 

" 

220.0      " 

3-13    " 

H 

20 

44-5 

-5 

" 

232.0      " 

3-30    " 

u 

30 

42.5 

-5 

u 

243.2      « 

3.46    « 

" 

40 

40.9 

-5 

u 

253-1 

3-6o     ' 

M 

g 

39-7 
38.9 

-5 

-5 

u 

« 

260.1      " 
265.0      " 

3.70    « 
3-77 

" 

70 

39-° 

-5 

« 

264.3      " 

3-76    « 

" 

80 

39-6 

~5 

H 

260.8      " 

3-71 

«                    (( 

90 

40.2 

-5 

« 

257-3  ; 

3.66    " 

«(                    « 

100 

41.0 

-5 

U 

252.4  «•  . 

3-59    ' 

TABLE  94. 


COMPRESSIBILITY   AND    BULK    MODULI   OF   SOLIDS. 


Solid. 

Compression 
per  unit  vol- 
ume per  atmo. 
Xio6. 

Authority. 

Calculated  values  of 
bulk  modulus  in  — 

Grammes 
per  sq.  cm. 

Pounds 
per  sq.  in. 

1-93 
0-747 
1.  2O 
1.  14 
2.67 
4-2t 

7-45t 
0.61 
0.113 

o-95 
0.86 
i.  02 
2.76 
0.68 
2.2-2.9 

VoSgt  .     . 

u 
u 

I 

Amagat  . 
Buchanan 
Amagat   . 

535  X  io« 
i3»4    ' 

906    " 

387  ;; 
246 

i$  : 
1694 

9140  * 
1090  * 

1202        ' 
IOI2        ' 

374     ' 
1518     ' 

405' 

7.61  X  io6 

19.68      " 
12.24     " 
12.89     " 
5-50      " 
3-50      " 

i-97    ' 
24.11 
130.10    " 
15.48    " 
17.10    ' 
14.41     " 

5-32  ;; 

21.61     " 

5.76  « 

Beryl       

Fluorspar        

Rock  salt    .          .... 

Topaz                   .... 

Tourmaline     

Lead                                            •     •     • 

Steel                         

r;iqco 

*  Tait  finds  for  fresh  water  the  value  .0072  (i  -o.o34/)  and  for  sea  water  .00666  (i  -o.o34/)  where/  is  the  pres- 
sure in  tons  per  square  inch.     The  range  of  variation  of  /  was  from  i  to  3  tons. 

t  Rontgen  and  Schneider  by  piezometric  experiments  obtained  5-0  X  io-«  for  rock  salt  and  5-6  X  10- 
(Wied.  Ann.,  vol.  31). 
SMITHSONIAN  TABLES. 


TABLE  95. 

DENSITY  OR  MASS  IN  GRAMMES  PER  CUBIC  CENTIMETRE  AND  POUNDS 
PER  CUBIC   FOOT  OF  VARIOUS  SOLIDS.* 


Substance. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
foot. 

Substance. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
fooc. 

Agate  .... 

2.5-2.7 

156-168 

Gas  carbon  . 

i.  88 

119 

Alabaster  : 

Glass  : 

Carbonate 

2.69-2.78 

168-173 

Common  .        .        . 

2.4-2.8 

150-175 

Sulphate  .         .        . 

2.26-2.32 

I4I-I45 

Flint          .         .         . 

2-9-4-5 

180-280 

Alum,  potash       , 

1.7 

106 

Glauber's  salt 

1.4-1.5 

87-93 

Amber          .         . 

I.06-I.II 

66-69 

Glue     .         .  . 

1.27 

80 

1  Anthracite  . 

I.4-I.8 

87-112 

Gneiss          .        , 

2.4-2.7 

150-168 

Apatite 

3.16-3.22 

197-201 

Granite         .         .        ." 

2-5-3-0 

156-187 

Aragonite    .         ... 

3-° 

I87 

Graphite 

1.9-2.3 

120-140 

Arsenic 

5-7-5-72 

356-358 

Gravel          .  '     ;  '     . 

1.  2-1.8 

94-112 

Asbestos 

2.0-2.8 

125-175 

Gray  copper  ore 

4-4-5-4 

275-335 

Asphaltum  . 

1.1-1.2 

69-75 

Green  stone 

2.9-3.0 

180-185 

Barite  .... 

4-5 

28l 

Gum  arabic 

1.3-1.4 

80-85 

Basalt 

2.7—7  I 

168—197 

Gunpowder  : 

Beeswax 

*•/    J-1 

0.96-0.97 

60-6  1 

Loose 

0.9 

56 

Bole     .... 

2.2-2-5 

137-156 

Tamped   . 

J-75 

109 

Bone    .... 

1.7-2.0 

106-125 

Gypsum,  burnt    .         . 

i.Si 

Boracite 
Borax            .         . 

2-9-3-0 
1.7-1.8 

181-187 
I06-II2 

Hornblende 
Ice       .... 

0.88-0.91 

187 

55-57 

Borax  glass 

2.6 

162 

Iodine 

4-95 

3°9 

Boron            . 

2.68-2.69 

167-168 

Ivory   .        . 

1.83-1.92 

114-120 

Brick   .         .        % 

2.O-2.2 

125-137 

Kaolin 

2  ° 

137 

Butter  .... 

0.86-0.87 

53-54 

Lava  : 

Calamine     . 
Calcspar 

4-1-4-5 

2.6-2.8 

255-280 
162-175 

Basaltic    . 
Trachytic 

2.8-3.0 
2.0-2.7 

175-185 
125-168 

Carbon. 

Lead  acetate 

2.4 

150 

See  Graphite,  etc. 

Leather  : 

Caoutchouc        •'..'-'     . 

0.92-0.99 

57-62 

Dry       •    .     •-:.,     ... 

0.86 

54 

Celestine      . 

3-9 

243 

Greased    . 

1.02 

64 

Cement  : 

Lime  : 

Pulverized  loose 

1.15-1.7 

72-105 

Mortar 

1.65-1.78 

103-111 

Pressed     . 

1.85 

"5 

Slaked      . 

I.3-I.4 

81-87 

Set    .... 

2.7-3.0 

168-187 

Lime    . 

2-3-3-2 

144-200 

Cetin    .        .         .         . 

0.88-0.94 

55-59 

Limestone    . 

2.46-2.86 

154-178 

Chalk  .         . 

1.9-2.8 

118-175 

Litharge  : 

Charcoal  : 

Artificial  . 

9-3-9-4 

580-585 

Oak          ,         .         . 

o-57 

35 

Natural    . 

7-8-8.0 

489-492 

Pine          .         .         . 

0.28-0.44 

I7"5-27-5 

Magnesia     .         ... 

3-2 

200 

Chrome  yellow    . 

6.00 

374 

Magnesite    . 

187 

Cinnabar      .        .        » 
Clay     .... 

8.12 

1.8-2.6 

507 
122-162 

Magnetite    .         .  •     -. 
Malachite     .         .        . 

4.9-5.2 

3-7-4-1 

306-324 
231-256 

Clayslate     .        .        . 

2.8-2.9 

175-180 

Manganese  : 

Coal,  soft     .       \.    '     . 

1.2-1.5 

75-94 

Red  ore    . 

3-46 

216 

Cobaltite     .        .        . 

6-4-7-3 

400-455 

Black  ore 

3-9-4-1 

243-256 

Cocoa  butter 
Coke    .... 

0.89-0.91 
1.0-1.7 

56-57 
62-105 

Marble 
Marl     .... 

2.5-2.8 
1.6-2.1; 

157-177 
100-156 

Copal  .         .         .        . 

1.04-1.14 

65-71 

Masonry 

1.85-23 

116-144 

Corundum  .        . 

3.9-4.0 

245-250 

Meerschaum 

.99-1.28 

61.8-79.9! 

Diamond      . 

3-5-3-6 

220-225 

Melaphyre   . 

2.6 

162 

Anthracitic 

j.66 

104 

Mica    .'        . 

2.6-3.2 

165-200 

Carbonado 

3-01-3-25 

188-203 

Mortar 

1.75 

109 

Diorite         .         .      „  .- 

2.8-3.1 

I75~I93 

Mud     .... 

1.6 

IO2 

Dolomite     .        . 

3.8-2.9 

175-181 

Nitroglycerine 

1.6 

99 

Earth,  dry   .        .       .  .  "• 

1.6-1.9 

100-120 

Ochre  .... 

3-5 

218 

Ebonite        .         .     "    .''. 

I-I5 

72 

Opal     .... 

2.2 

*37 

Emery          .         .         . 

4.0 

250 

Orpiment     . 

3-4-3-5 

212-218 

Epsom  salts  : 

Paper  .... 

0.7-1.15 

44-72 

Crystalline 

1.7-1.8 

106-112 

Paraffin 

0.87-0.91 

54-57 

Anhydrous 

2.6 

162 

Peat     .... 

0.84 

52 

Feldspar 

2.53-2.58 

158-161 

Phosphorus,  white 

1.82 

114 

Flint    .... 

2-63 

164 

Pitch    .... 

1.07 

67 

Fluor  spar  . 
Gabronite    . 

3.14-3.18 
2-9-3-0 

196-198 
181-187 

Porcelain 
Porphyry 

2-3-2-5 
2.6-2.9 

i  43-1  56 
162-181 

Gamboge     . 

1.2 

75 

Potash          .         .     '     . 

2.26 

141 

Galena 
Garnet 

7-3-7-6 
3.6-3.8 

460-470 

Pyrites 
Pyrolusite    . 

4-9-5-2 
3-7-4-6 

306-324 
231-287 

SMITHSONIAN  TABLES. 


For  metals,  see  Table  97. 


84 


DENSITY  OF  VARIOUS  SOLIDS. 


TABLE  95, 


Substance. 


Grammes 
per  cubic 
centimetre. 


Pounds 

per  cubic 

foot. 


Substance. 


Grammes 
per  cubic 
centimetre. 


Pounds 

per  cubic 

foot. 


Pumice  stone 
Quartz 
Resin   . 
Rock  crystal 
Rock  salt     . 
Sal  ammoniac 
Saltpetre 
Sand: 

Dry  . 

Damp 

Sandstone    . 
Selenium 
Serpentine  . 
Shale  . 
Silicon 

Siliceous  earth 
Slag, furnace 
Slate    . 
Snow,  loose 


0.37-0.9 
2.65 
1.07 

2.6 

2.28-2.41 

1.5-16 

1.95-2.08 

1.40-1.65 
1.90-2.05 

2.2-2.5 

4.2-4.8 

2.43-2.66 

2.6 

2.0-2.15 

2.66 
2-5-3-0 
2.6-2.7 

0.125 


23-56 

'65 

67 

162 

142-150 
94-100 
122-130 

87-103. 
119-128 
137-156 
262-300 
152-166 

162 
125-156 

1 66 

156-187 
162-168 

7.8 


Soapstone,  Steatite 
Soda: 

Roasted   . 

Crystalline 
Spathic  iron  ore 
Starch 
Stibnite 
Strontianite 
Syenite 
Sugar  . 
Talc     . 
Tallow 
Tellurium     . 
Tile      . 
Tinstone 
Topaz 
Tourmaline 
Trachyte 
Trap     . 


2-5 
i-45 

3-7-3-9 
'•53 

4-6-4-7 


1.61 

2.7 
.9i-.97 

6.38-6.42 
1.4-2.3 
6.4-7.0 
3-5-3-6 

2.94-3.24 
2.7-2.8 
2.6-2.7 


162-175 

156 

90 

231-243 

287-293 

231 

162 

100 

1 68 

570-605 
398-401 
87-143 
399-437 
219-223 
183-202 
168-175 
162-170 


TABLE  96. 

DENSITY  OR  MASS  IN  GRAMMES  PER  CUBIC  CENTIMETRE  AND  POUNDS 
PER  CUBIC  FOOT  OF  VARIOUS  ALLOYS  (BRASSES  AND  BRONZES). 


Alloy. 


Grammes 
per  cubic 
centimetre. 


Pounds 

per  cubic 

foot. 


Brasses  :  Yellow,  7oCu  +  3oZn,  cast 8.44               527 

rolled  ......  8.56               534 

"                 "                  "              drawn          .        .        .        .        .  8.70               542 

Red,  goCu  +  loZn           .        .        .        .        .        .        .  8.60               536 

White,  soCu  +  foZn       .        .        1        .        .        .        .  8.20               511 

Bronzes:  goCu -f  loSn  .        .        .        .                .        .        .        .  8.78               548 

"          85Cu -j-  i5Sn 8.89               555 

SoCu  +  2oSn 8.74               545 

75Cu  +  25Sn 8.83               551 

German  Silver:  Chinese,  26-3Cu  +  36.6Zn  +  36.8  Ni  .         .         .  8.30               518 

Berlin  (i)  52Cu  +  26Zn  +  22Ni  ....  8.45               527 

"            «             "      (2)  59Cu  -f  3oZn  -j-  iiNi.        .        .        .  8.34 

«            "             "      (3)  63Cu  -f  3oZn  -j-  6Ni    ....  8.30               518 

Nickelin 8.77               547 

LeadandTn:  87-5Pb+  i2-5Sn 10.60 

84Pb+i6Sn          .......  10.33               644 

77.8Pb  +  22.2Sn 10.05              627 

63.7  Pb -j- 36,3811 9-43              588 

46.7Pb  +  53-3Sn 545 

"        «              3O-5Pb  -J-  69-5Sn °-24 

Bismuth,  Lead,  and  Tin  :  5361  +  4oPb  +  7Cd      .        .        .        .  10.56 

Wood's  Metal:  5oB5  +  25?b  +  i2-5Cd  +  i2.5Sn        .        .        .  9-7Q 

Cadmium  and  Tin  :  32Cd+  68Sn 

Gold  and  Copper :  98Au  +  2Cu 

96Au  +  4Cu l8-36 

94Au4-6Cu 17-95             "20 

o->Au  +  8Cu *7-S2             I093 

9oAu  +  loCu I7-JO 

88Au  +  i2Cu l6-8i             1049 

86Au  +  i4Cu -  l6-47             1027 

Aluminium  and  Copper  :  loAl  +  9oCu 

«  "          "  sAl  +  95Cu 

«  «          «<  -jAl  -f-  97Cu 

Aluminium  and  Zinc:  91  Al  +  gZn 

Platinum  and  Iridium  :  9oPt  +  loir 

85Pt+i5lr 21.62              1348 

66.67Pt  +  33.33Tr 21.87             1364 

5Pt  +  95lr 22.38             1396 


SMITHSONIAN  TABLES. 


TA3LE    97. 

DENSITY   OR    MASS  IN   GRAMMES   PER   CUBIC   CENTIMETRE  AND 
POUNDS   PER   CUBIC    FOOT   OF  THE    METALS.* 

When  the  value  is  taken  from  a  particular  authority  that  authority  is  given,  but  in  most  cases  the  extremes  or  average 

from  a  number  of  authorities  are  given. 


Metal. 

Physical  state. 

Grammes  per 
cubic  centi- 
metre. 

Pounds  per 
cubic  foot. 

Temp.C.tl 

Authority. 

Aluminium.     .     . 

Cast       .     .     . 

2.56-2.58 

l6o-l6l 

Wrought  .     . 

2.65-2.80 

165-175 

Antimony    . 

Solid     .     .     . 

6.70-6.72 

418-419 

Amorphous   . 

About  6.22 

388 

Barium    .... 

— 

3.75-4.00 

234-250 

. 

Bismuth  .... 

Solid     .     .     . 

9.70-9.90 
9-673 

605-618 
604 

271 

)  Vincentini  and 

u       \-\\\ 

Liquid  .     .     . 

IO.OO4 

624 

271 

[      Omodei. 

Cadmium     .     .     . 

Cast      .     .     . 

8.54-8.57 

533-535 

Wrought  .     . 

8.670 

«« 

Solid     .     .     . 

8.366 

522 

318 

{  Vincentini  and 

"    !  .  .  . 

Liquid  .     .     . 

7.989 

498 

318 

f      Omodei. 

Caesium.     .     .     . 

— 

I.88-I.90 

117 

Calcium  .... 

— 

1.580 

98.6 

Cerium    .... 

— 

6.62-6.72 

475-482 

Chromium  .     .     . 

— 

6.52-6.73 

407-420 

Cobalt    .... 

Cast      .     .     . 

8.50-8.70 

530-542 

u 

Wrought  .     . 

9-IOO 

563 

Columbium      .     . 

Liquid  .     .     . 

7.10-7.40 

443-462 

Copper   .... 

Cast      .     .     . 

8.80-8.95 

549-558 

Wrought  .     . 
Liquid  .     .     . 

8.85-8.95 
8.217 

552-558 
513 

Roberts  &  Wrightson. 

Didymium  .     .     . 
Gallium  .... 

— 

6.540 
5-930 

408 
37° 

24 

Lecoq  de  Boisbaudran. 

Germanium     .     . 

— 

5.460 

341 

2O 

Winkler. 

Glucinium  .     .     . 



1.86-2.06 

116-127 

Gold            .     .     . 

Cast      .     .     . 

19.26-10.^4 

1202-1207 

Wrought  .     . 

.7            y  o* 

I9-33~I9-34 

1207 

Indium   .... 

— 

7.27-7.42 

454-463 

Iridium   .... 

— 

21.78-22.42 

I359~I399 

Iron 

Gray  cast  . 

7.03-7.13 

4^9-445 

« 

White  cast    . 

7.^8—7.77 

Jy       o 

473-402 

u 

Wrought  . 

/  j     /  /  j 
7.80-7.90 

485-493 

H 

Liquid  . 

6.880 

429 

Roberts  &  Wrightson. 

Lanthanum      .     . 

6.05-6.16 

377-384 

Hildebrand  &  Norton. 

Lead 

Cast      .     .     . 

1  1  .  740 

708 

24 

Reich. 

Wrought  . 

j^ 
11.360 

700 

^*T- 

24 

„ 

Solid     .     .     . 

11.005 

686 

**T- 
725 

1  Vincentini  and 

H 

Liquid  . 

10.645 

664 

O    D 

[     Omodei. 

Lithium  .... 

0.590 

39 

Magnesium      .     . 
Manganese  .     .     . 



1.69-1.75 
6.86-8.03 

105-109 
428-501 

"          ... 

— 

Av.  abt.  7.4 

462 

Mercury  .     .^   .     . 

— 

I3-596 

848 

Molybdenum   .     . 

— 

8.40-8.60 

524-536 

Nickel     .... 

— 

8.30-8.90 

5'7-555o 

Osmium.     .     .     . 

— 

21.40-22.40 

1  335-  *  398 

Palladium   .     .     . 

— 

II.OO-I2.OO 

686-749 

Platinum     .     .     . 

— 

2I.2O-2I.7O 

1322-1354 

Potassium    .    . 

Solid     .     .     . 

0.86-0.88 

54-55 

"         |  .'  •  *••   . 

Solid     .     .     . 

0.8510 

53-7 

62.1 

)  Vincentini  and 

"           .    .    . 

Liquid  .     .     . 

0.8298 

53-8 

62.1 

}      Omodei. 

Rhodium     .    '.  •  > 

— 

II.OO-I2.IO 

686-755 

Ruthenium  .     .     . 

— 

II.OO-II.4O 

686-711 

Silver      .... 

Cast.     .     .     . 

10.40-10.50 

649-655 

.  !  !  1 

Wrought  .     . 
Liquid  .     .     . 

10.55-10.57 
9.500 

658-659 
593 

Roberts  &  Wrightson. 

*  This  table  has  been  to  a  large  extent  compiled  from  Clark's  "  Constants  of  Nature,"  and  Landolt  &  Bbrnstein's 
"Phys.  Chem.  Tab-" 

t  When  the  temperature  is  not  given,  ordinary  atmospheric  temperature  is  to  be  understood. 
SMITHSONIAN  TABLES. 

86 


TABLE  97, 

DENSITY  OR    MASS   IN   GRAMMES  PER  CUBIC  CENTIMETRE   AND 
POUNDS   PER    CUBIC   FOOT   OF   THE   METALS. 


Metal. 

Physical  state. 

Grammes  per 
cubic  centi- 
metre. 

Pounds  per 
cubic  foot. 

* 

0 

1 

Authority. 

Sodium  .... 

it 

Strontium  .  .  . 
Thallium  .  .  . 
T  n 

Solid     .     .     . 
Liquid  . 
At  boiling  pt. 

Cast 

0.97-0.99 
0.9519 
0.9287 
0.7414 
2.50-2.58 
II.8-II.9 

605-618 

59-4 
58.0 
46.3 
156-161 
736-742 

97.6 
97.6 

)  Vincentini  and 
)      Omodei. 
Ramsay. 
Matthieson. 

< 

Wrought  .  . 
Crystallized  . 

.^y<j 
7.300 
f\  Q7—  7  18 

455 
455 

i 

Solid 

7  l8^C 

226 

Titanium  t  .  .  . 
Thorium-}  .  .  . 
Tungsten  .  .  . 
Uranium  .  .  . 
Zinc 

Liquid  .  .  . 
Cast 

76$ 

5-30° 
9.4-10.1 
19.120 
18.33-18.65 

454 
436 
341 
587-630 

"93 
1143-1163 

226 

)      Omodei. 
Roscoe. 

Wrought  .  . 
Liquid 

7.190 
6480 

4jy^44/ 
449 

AQA 

Roberts  &  Wrightson 

Zirconium  .  .  . 

4.140 

258 

Froost. 

TABLE  98. 

MASS    IN    GRAMMES    PER    CUBIC   CENTIMETRE    AND    IN    POUNDS    PER 
CUBIC    FOOT    OF    DIFFERENT    KINDS    OF    WOOD. 

The  wood  is  supposed  to  be  seasoned  and  of  average  dryness. 


Wood. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
foot. 

Wood. 

Grammes 
per  cubic 
centimetre. 

Pounds 
per  cubic 
foot. 

Alder   
Apple  
Ash      
Basswood.    See  Linden. 
Beech 

0.42-0.68 
0.66-0.84 
0.65-0.85 

0.70-0.90 
0.84. 
0.51-0.77 
0.95-1.16 
I.O5 
0.38 
0.40-0.57 
0.70-0.90 
O.22-O.26 

i.n-i-33 

0.54-0.60 

0.35-0.50 
0.50-0.56 
0.83-0.85 
0.48-0.70 

0.43-°-  53 
0.48-0.70 
0.37-0.60 

26-42 
4I-52 
40-53 

43-56 

32-48 
59-72 

65 
24 

30-35 
43-56 
14-16 
69-83 

34-37 

22-31 
3i-35 
52-53 
3°-44 
27-33 
30-44 
23-37 

Greenheart   

0.93-1.04 
O.6b-O.8o 
0.60-0.93 
1.03 
0.92 

0.68-1.00 

i-i7-i-33 
0.32-0.59 
0.67-0.71 
0.56 
0.85 
0.62-0.75 
0.60-0.90 
0.61-0.73 
0.66-0.78 
o-35-o-5 
o-95 
0.40-0.60 
0.66-0.88 
0.98 
0.64-0.70 

1.  00 

0.40-0.60 

58-65 

37-49 
37-58 
64 

42-62 

73-83 
20-37 
42-44 
35 
53 
39-47 
37-56 
3M5 
41-49 
22-31 

59 
24-37 
41-55 
61 

40-43 
62 

24-37 

Hazel  

'   Hickory   .     .              . 

Iron-bark 

Laburnum     

Birch    

Lignum  vitae     .... 
Linden  or  Lime-tree  .     . 
Locust      .... 

Box                     .          .     . 

Bullet  tree    

Mahogany,  Honduras    . 
"            Spanish   .     . 

Cedar  
Cherry 

Cork 

Oak      
Pear-tree  

Elm      
Fir  or  Pine,  American 
White 
Larch  .     . 
"              Pitch    .     . 
"              Red      .     . 
"              Scotch      . 
"              Spruce 
Yellow     . 

Plum-tree          .... 

Poplar 

Teak,  Indian     .... 
'•      African   .... 
Walnut               .... 

Willow                    •     •     • 

*  When  the  temperature  is  not  given,  ordinary  atmospheric  temperature  is  to  be  understood. 

t  The  density  of  titanium  is  inferential,  and  actual  determination  a  year  or  two  ago  gave  a  lower  value. 

t  The  lower  value  for  thorium  represents  impure  material. 

SMITHSONIAN  TABLES. 


TABLE  99. 


DENSITY   OF    LIQUIDS. 


Density  or  mass  in  grammes  per  cubic  centimetres  and  in  pounds  per  cubic  foot  of  various  liquids. 


Liquid. 

Grammes  per 
cubic  centimetre. 

Pounds  per 
cubic  foot. 

Temp.  C. 

Acetone         .        .        ,        .        . 

0.792 

49-4 

0° 

Alcohol,  ethyl       .        .        .        ..-.      . 

0.791 

49-4 

o 

"         methyl    .        . 

0.810 

5°-5 

o 

"         proof  spirit     .         .        .        . 

0.916 

57-2 

0 

Anilin             .         .         ,         . 

1-035 

64-5 

o 

Benzene         

0.899 

56.1 

o 

Bromine         ........ 

3-187 

199.0 

o 

59.2-60.2 

I  q 

Carbon  disulphide         ,        .        .         .         . 

1.293 

80.6 

15 

Chloroform   ........ 

1.480 

92-3 

18 

Ether     .                                 

0.736 

45-9 

0 

Glycerine      .        .        .        .        .        . 

1.260 

78.6 

0 

Mercury         .        .        .        .        . 

13.596 

836.0 

o 

Naphtha  (wood)    

0.848-0.810 
0.665 

52-9-50-5 
41.5 

o 
I  ? 

Oils  :   Amber         

0.800 

49-9 

•  J 

15 

Anise-seed  

0.996 

61.1 

16 

Camphor    

0.910 

56.8 

— 

Castor         .        

0.969 

60.5 

15 

Cocoanut    

0.925 

57-7 

15 

Cotton  seed        

0.926 

60.2 

16 

Creosot       

1.040-1.100 

64.9-68.6 

15 

Lard   .         ..... 

0.920 

57-4 

Lavender    .        ,  ,      

0.877 

54-7 

16 

Lemon         

0.844 

52-7 

16 

Linseed  (boiled)          

0.942 

58.8 

15 

Mineral  (lubricating)  

0.900-0.925 

56-2-57-7 

20 

Olive  

0.918 

57-3 

15 

Palm  . 

0.905 

56-5 

15 

Pine    .         .         .        . 

0.850-0.860 

53-o-54-o 

15 

Poppy          

0.924 

57-7 

Rapeseed  (crude)       

0.915 

15 

"        (refined)       .''.'. 

O.QI'? 

57.0 

I  c 

Resin          

J    3 

o-955 

59-6 

J 
15 

Train  or  Whale  .        .  •  '    • 
Turpentine          

0.918-0.925 

0-873 

57-3-57-7 

:i 

0.06  S 

60  ? 

16 

;/     J  i 

0.878 

54.8 

o 

(light)  
Pyrol  igneous  acid          

0.795-0.805 
0.800 

49.6-50.2 
49-9 

15 

0 

i  .02  c 

64  o 

I  e 

I.2IO 

WT-.W 

7  r  r 

1  j 

17 

Water    

I.OOO 

/oo 

62.4 

1  / 

4 

SMITHSONIAN  TABLES. 


88 


TABLE  1 0O 


DENSITY   OF   CASES. 


The  following  table  gives  the  specific  gravity  of  gases  at  o°  C.  and  76  centimetres  pressure  relative  to  air  at  o°  and 
76  centimetres  pressure,  together  with  their  mass  in  grammes  per  cubic  centimetre  and  in  pounds  per  cubic  foot. 


Gas. 

Sp.  gr. 

Grammes  per 
cubic  centimetre. 

Pounds  per 
cubic  foot. 

Air    '. 

Ammonia      t  •    ,'r       .        .        .        .        . 
Carbon  dioxide         

I.OOO 

0.597 
1.529 
0.067 

0.001293 
0.000770 
0.001974 
0.001°  ^4 

0.08071 
0.04807 
0.12323 

O.O77O4 

Chlorine    . 

(  from 

2.422 
0.320 

0.003133 
0.000414 

0.19559 
0.02583 

(to 

0.740  . 
i.  806 

0.000957 
O.OO277O 

0.05973 
0.14546 

Hydrofluoric  acid     

2.370 
1  .2  W 

O.OO2937 

0.001616 

0.18335 
0.10088 

0.0696 

0.000090 

o.oo  562 

I.I9I 

0.001476 

0.09214 

O.^Q 

0.000727 

0.04538 

0.972 

0.001257 

0.07847 

i.  0^9 

0.001343 

0.08384 

Nitrous  oxide,  N2O  .         .        .        .        •        « 

i-527 

I.  IOC 

0.001970 
0.001430 

0.12298 
0.08927 

2.247 

0.002785 

0.17386 

0.469 

0.000581 

0.03627 

SMITHSONIAN   TABLES. 


89 


TABLE  101. 


DENSITY   OF   AQUEOUS   SOLUTIONS.* 


The  following  table  gives  the  density  of  solutions  of  various  salts  in  water.     The  numbers  give  the  weight 
grammes  per  cubic  centimetre.     For  brevity  the  substance  is  indicated  by  formula  only. 


Substance. 

Weight  of  the  dissolved  substance  in  100  parts  by  weight  of 
the  solution. 

0 

cL 

Authority. 

5 

10 

15 

20 

=5 

3° 

4° 

50 

60 

K2O  .... 

1.047 

1.098 

i-i53 

I.2I4 

1.284 

1-354 

!-5°3 

1.6^9 

1.809 

15- 

Schiff. 

KOH      .     .     . 

1.040 

1.082 

1.027 

I.O76 

1.229 

1.286 

1.410 

I-538 

1.666 

" 

Na20      .     .     . 
NaOH    ... 

1.073 

1.058 

I.I44 
I.II4 

1.218 
1.169 

1.284 
1.224 

1-354 
1.279 

1.421 
1.331 

1-557 
1.436 

1.689 
!-539 

1.829 
1.642 

*5- 

M 

NH3  .... 

0.9/8 

0.949 

0.940 

0.924 

0.909 

0.896 

- 

- 

16. 

Carius. 

NH4C1   . 

I.OI5 

1.030 

1.044 

1.058 

1.072 

_ 

_ 

_ 

_ 

I5. 

Gerlach. 

KC1 

T  Oil 

1.065 

I  OQQ 

I        I    "*    ^ 

_ 

_ 

_ 

__ 

tm 

I  <\. 

(• 

NaCl.    .     .     . 

.°35 

1.072 

I.  IIO 

I.ICO 

1.191 

_ 

_ 

_ 

_ 

J 

« 

LiCl  .... 

.029 

1-057 

1.085 

1.116 

1.147 

1.181 

J.255 

- 

- 

15. 

it 

CaCl2     .     .    . 

.041 

1.086 

1.132 

1.181 

1.232 

1.286 

.402 

- 

- 

15- 

" 

CaCl2  +  6H20 

.019 

I.O4O 

1.  06  1 

1.083 

1.105 

1.128 

.176 

1.225 

1.276 

1  8. 

Schiff. 

A1C13      .     .     . 

•°35 

1.072 

I.  Ill 

l-*S3 

1.196 

1.241 

-340 

— 

15. 

Gerlach. 

MgCl2    .     .     . 

.041 

1.085 

1.130 

1.177 

1.226 

1.278 

_ 

_ 

15. 

" 

MgCl2+6H2O 
ZnCl2      .     .     . 

.014 
•043 

1.032 
1.089 

1.049 

1.067 
1.184 

1.085 
1.236 

1.103 
1.289 

.141 
.417 

1.183 
1-563 

1.222 

i-737 

24. 
19-5 

Schiff. 
Kremers. 

CdCl2     .    .    . 

1.043 

1.087 

1.138 

i.r93 

1.254 

I.3!9 

1.469 

1-653 

1.887 

19-5 

« 

SrCl2.    .    .     . 

1.044 

1.092 

1-143 

1.198 

1.257 

I.32I 

— 

— 

- 

Gerlach. 

SrCl2-f  6H2O 

1.027 

!.°53 

1.082 

i.  in 

1.042 

I.I74 

1.242 

1.317 

_ 

I5- 

M 

BaCl2     .     .     . 
BaCl2+2H20 

1.045 

1.094 
1.075 

1.147 

1.119 

1.205 
1.166 

1.269 
1.217 

1-273 

"* 

- 

- 

21. 

Schiff. 

CuCl2     .    .     . 

1.044 

1.091 

1-155 

1.  221 

1.291 

1.360 

i-527 

_ 

- 

17.5 

Franz. 

NC12.    .    .    . 

1.048 

1.098 

1.157 

1.223 

1.299 

— 

— 

— 

17-S 

" 

HgCl2     .     .     . 

I.O4I 

1.092 

— 

_ 

_ 

_ 

20. 

Mendelejeff. 

Fe2Cl6    .     .     . 

I.O4I 

i.  086 

1.130 

I.I79 

1.232 

I.29O 

1.413 

1-545 

1.668 

17.5 

Hager. 

PtCl4.     .     .    . 

T  O46 

T  OO*7 

1.153 

I.2I4 

1    ^R  C 

1.762 

1.546 

I  78  c 

_ 

Precht. 

SnCl2+2H2O 
SnCl4+5H2O 

1.032 
1.029 

1.067 
1.058 

1.104 
1.089 

1.  122 

1.185 
i.i57 

i     JV>~ 

1.229 
1-193 

1.329 

1.274 

/      J 

1.444 

1.365 

1.580 
1.467 

15- 

Gerlach. 

LiBr  .... 

I-°33 

1.070 

I.  Ill 

I.I54 

1.202 

1.252 

1.366 

1.498 

- 

19-5 

Kremers. 

KBr  .... 

1-073 

1.114 

LI57 

I.2O5 

1.254 

1.364 

- 

" 

NaBr      .     .     . 

1.038 

1.078 

1.123 

I.I72 

1.224 

1.279 

1.408 

!.563 

- 

19-5 

" 

MgBr2    .     .     . 

1.041 

1.085 

I>135 

1.189 

1.245 

1.308 

1.449 

1.623 

_ 

'9-5 

u 

ZnBr2     .     .     . 

1.043 

1.091 

I.I94 

I.2O2 

1.263 

1.328 

J-473 

1.648 

1-873 

i9-5 

H 

CdBr2     .     .     . 

1.041 

i.  088 

1.139 

I.I97 

1.258 

1.324 

1.479 

1678 

19-5 

" 

CaBr2     .     .     . 

1.042 

1.087 

1.137 

I.I92 

2.250 

1-313 

1-459 

1.639 

- 

19-5 

" 

BaBr2     .     .     . 

1.043 

1.090 

I.I42 

I.I99 

1.260 

1.327 

1.483 

1.683 

- 

19-5 

It 

SrBr2      .     .     . 

1.043 

1.089 

I.I40 

I.I98 

1.260 

1.328 

1.489 

1.693 

i-953 

T9-5 

It 

KI      .... 

T  O76 

1.076 

1.118 

I.l64 

1.216 

I  °OQ 

r  Q     r 

It 

Lil      .... 

1.036 

1.077 

1.  122 

*        WT- 

1.170 

1.222 

L.'.Vy 
1.278 

1.412 

!-573 

1-775 

19-S 

« 

Nal    .... 

T  038 

i.  080 

I.I26 

1.177 

T    1?'5'7 

1.292 

i.  808 

« 

ZnI2   .     .    . 

1.043 

1.089 

1.138 

/  / 

1.194 

L253 

1.366 

1.418 

1.648 

1.873 

19-5 

" 

CdI2  .... 

1.042 

i.  086 

1.136 

1.192 

1.251 

i-3'7 

1.474 

1.678 

_ 

T9-5 

H 

MgI2.     .     .     . 

1.041 

i.  086 

I-I37 

1.192 

1.252 

1.318 

1.472 

1.666 

1.913 

19-5 

" 

CaI2  .... 

i.  088 

1.178 

1.196 

1.258 

I.7IQ 

1.47  ^ 

1.667 

I.QOS 

IQ.C; 

<< 

SrI2    .... 

1.043 

1.089 

.  1  JU 

1.140 

1.198 

1.260 

*•  J  *  7 
1.328 

X"4Y  j 
1.489 

*'WJ 

1.693 

;/ 

J-953 

y  *) 

19-5 

" 

BaI2  .... 

1.043 

1.089 

1.141 

1.199 

1.263 

1-331 

M93 

1.702 

1.968 

19-5 

« 

NaClOg  .     .     . 

1-035 

i.  068 

1.106 

1.145 

1.188 

1-233 

1.329 

_ 

_ 

I9.5 

" 

NaBrO3  .     .     . 

1.039 

1.081 

1.127 

1.176 

1.229 

1.287 

_ 

— 

19.5 

H 

KN03     .     .     . 

1.031 

1.064 

1.099 

LI35 

_ 

_ 

_ 

_ 

15. 

Gerlach. 

NaNO3  .     .     . 

1.031 

1.065 

I.IOI 

I.I4O 

1.180 

1.222 

1.313 

1.416 

_ 

20.2 

Schiff. 

AgN03  .    .     . 

1.044 

1.090 

1.140 

-195 

I-255 

1.322 

1.479 

1-675 

1.918 

T5- 

Kohlrausch. 

*  Compiled  from  two  papers  on  the  subject  by  Gerlach  in  the  "  Zeit.  fur  Anal.  Chim.,"  vols.  8  and  27. 
SMITHSONIAN  TABLES. 

90 


DENSITY    OF    AQUEOUS    SOLUTIONS. 


TABLE  1O1 . 


Weight  of  the  dissolved  substance  in  100  parts  by  weight  of 

the  solution. 

u 

Substance. 

d 

E 

Authority. 

5 

10 

15 

20 

25 

30 

40 

5° 

60 

H 

NH4N08     .    .     . 

1.020 

I.O4I 

1.063 

1.085 

I.IO7 

I.I3I 

.178 

1.229 

1.282 

17-5 

Gerlach. 

ZnNO3    .... 

1.048 

1.095 

1.146 

1.  201 

1.263 

I-325 

•456 

_ 

'7-5 

Franz. 

ZnN03+6H20     . 

- 

1.054 

- 

I.II3 

- 

1.178 

.250 

1.329 

- 

14. 

Oudemans. 

Ca(N03)2    .     .     . 

1-037 

1-075 

I.llS 

I.I62 

1.  211 

1.260 

•367 

1.482 

1.604 

17-5 

Gerlach. 

Cu(N03)2    .     .     . 

1.044 

1.093 

I-I43 

1.203 

1.263 

1.328 

•47  1 

- 

Franz. 

Sr(N03)2     .     .     . 

1.039 

1.083 

1.129 

I.I79 

'     - 

- 

- 

- 

- 

!9-5 

Kremers. 

Pb(N03)2     .     .     . 

1.043 

1.091 

I.I99 

1.262 

I-332 

— 

— 

- 

17-5 

Gerlach. 

Cd(N03)2    .     •     • 

1.052 

1.097 

.150 

1.  212 

1.283 

J-355 

1.536 

1-759 

- 

17.5 

Franz. 

Co(N03)2     .     .     . 

1-045 

1.090 

•137 

I.I92 

1.252 

1.318 

1.465 

— 

17-5 

" 

Ni(NO3)2     .    .     . 

1.045 

1.090 

•137 

I.I92 

1.252 

1.318 

1.465 

- 

- 

17-5 

M 

Fe2(N03)6  .     .     . 

1.039 

1.076 

.117 

1.160 

I.2IO 

1.261 

1-373 

1.496 

1.657 

17-5 

u 

Mg(NO3)2+6H2O 
Mn(NO3)2+6H2O 

1.018 

1.025 

1.038 
1.052 

.060 
•079 

1.082 
I.I08 

I.IO5 
1.138 

1.129 
1.169 

1.179 

L235 

1.232 
1.307 

1-386 

21 

8 

Schiff. 
Oudemans. 

K2CO3    .... 

1.044 

1.092 

.141 

I.I92 

1.245 

1.300 

1.417 

!-543 

— 

15 

Gerlach. 

K2CO3+2H2O  . 

1-037 

1.072 

.no 

I.I5O 

I.I9I 

1.233 

1.320 

1.415 

1.511 

*5- 

" 

Na2CO3ioH2O     . 

1.019 

1.038 

•057 

1.077 

1.098 

1.118 

- 

- 

- 

15. 

" 

(NH4)2S04      .     . 
Fe2(S04)3    .     .     . 

1.027 
1.045 

1-055 
1.096 

.084 
.150 

I.II3 

1.207 

I.I42 
1.270 

1.170 
1-336 

1.226 
1.489 

1.287 

_ 

!89: 

Schiff. 
Hager. 

FeSCU  -{-  yHgO    . 

1.025 

I-°53 

.081 

I.  Ill 

I.I4I 

I-I73 

1.238 

— 

- 

17.2 

Schiff. 

TVTo"^O 

T  O  ^I 

1.104 

.161 

I  ^2  1 

1.284 

__ 

__ 

__ 

I  C 

Gerlach. 

MgSO  +7H2O   . 

I.O25 

1.050 

-075 

I.IOI 

I.I29 

I.I55 

1.215 

1.278 

_ 

0 

Na2So4  +  ioH2O 

I.OI9 

1.039 

•°59 

1.081 

1.  102 

1.124 

— 

— 

— 

15. 

" 

CuSO4+5H20   . 

I.O3I 

1.064 

.098 

1-134 

I-I73 

1.213 

- 

- 

- 

1  8. 

Schiff. 

MnSO4-(-4H2O  . 

I.O3I 

1.064 

1.099 

I.I74 

1.214 

1-303 

I-398 

— 

15. 

Gerlach. 

ZnSO4+7H2O    . 

I.O27 

I-°57 

1.089 

1.  122 

1.156 

1.191 

1.269 

I-35I 

1-443 

20.5 

Schiff. 

Fe2(SO)3+K2SO4 
+24H20.     .     . 

I.O26 

1.045 

1.066 

1.  088 

1.  112 

1.141 

_ 

_ 

_ 

17-5 

Franz. 

Cr2(SO)3+K2SO4 

+  24H20     .     . 

I.O16 

1.033 

1.051 

1.073 

1.099 

1.126 

1.188 

1.287 

1.454 

17-5 

" 

MgS04  +  K2S04 

+  6H20  .     .     . 

I.O32 

1.066 

I.IOI 

I.I38 

- 

- 

- 

- 

- 

'5- 

Schiff. 

(NH4)2S04  + 

FeS04  -f  6H2O 

1.028 

1.058 

1.090 

1.  122 

LI54 

1.191 

- 

- 

- 

19. 

" 

K2CrO4  .... 

1.039 

1.082 

1.127 

I.I74 

1.225 

1.279 

1-397 

- 

- 

x9-5 

K2Cr2O7      •     •     . 

r-°35 

1.071 

1.108 

_ 

_ 

- 

- 

- 

- 

19.5 

Kremers. 

Fe(Cy)6K4  .     .     . 

1.028 

1.059 

1.092 

I.I26 

- 

- 

- 

- 

- 

IS- 

Schiff. 

Fe(Cy)6K3  .     .     . 

1.025 

1-053 

1.145 

I.I79 

- 

- 

- 

- 

— 

13 

Pb(C2H302)2  + 
^HoO                  • 

I  OH 

1.064 

I.  ICO 

' 

1.177 

i.  220 

1.315 

1.426 

IS- 

Gerlach. 

2NaOH  +  As2O6 

*          /    / 

+  24H2O      .     . 

I.O2O 

1.042 

1.  066 

1.089 

I.II4 

1.140 

1.194 

— 

~ 

14. 

Schiff. 

5 

IO 

is 

20 

30 

40 

60 

80 

ICO 

SO 

1.040 

1084 

1.132 

I.I79 

1.277 

1.389 

1.564 

1.840 

_ 

J5- 

Brineau. 

SOo 

I.OI3 

1-033 
I.O2I 

J..\_>U^. 

1.028 
1.069 
1.047 

1.045 

2.104 
1.070 

* 

1.063 

I.I4I 
1.096 

.217 
.T50 

1.294 
1.207 

1.422 

1.506 

- 

4- 

Schiff. 
Kolb. 
Gerlach. 

C4H606  .... 

C6H807  .... 

I.OI8 

1.038 

1.058 

1.079 

.123 

1.170 

1-273 

- 

— 

IS- 

Cane  sugar  .     .     . 

I.OI9 

1.039 

.060 

1.082 

.129 

1.178 

1.289 

- 

- 

17-5 

" 

HC1    
HBr         .... 

1.025 

I.O50 

I.O71 

•075 
.114 

I.IOI 

1.158 

.257 

i.  200 
1.376 

_ 

_ 

_ 

14. 

Topsoe. 

HI       

I.O37 

*•  'w  l  O 

1.077 

.118 

1.165 

.271 

1.400 

- 

- 

- 

13- 

" 

H2SO4 

T  O12 

1.069 

.106 

1-145 

.223 

1.307 

1.501 

1.732 

1.838 

15. 

Kolb. 

H2SiFl6  .... 

T  040 

1.082 

1.077 

1-057 
1.056 
1.014 

1.127 
1.119 
i.  086 
i.  088 
i.  02  1 

»  *? 

I.I74 
1.167 
I.II9 
I.II9 
1.028 

•273 
.271 
.188 

I.O4I 

1-385 
1.264 
1.250 
1.052 

1.676 
1.438 

\-M 

1-459 
1-075 

1.528 

1-055 

17-5 
17-5 

Stolba. 
Hager. 
Schiff. 
Kolb. 
Oudemans. 
1 

P205  
HNO.     .     .     .     . 

!-035 

1.027 

T  028 

C2H402  .... 

I.OO7 

SMITHSONIAN  TABLES. 


TABLE  1O2. 

DENSITY    OF    WATER    AT    DIFFERENT    TEMPERATURES    BETWEEN    Oc 

AND    32°   C.* 


The  following  table  gives  the  relative  density  of  water  containing  air  in  solution,  —  the  maximum  density  of  water 
free  from  air  being  taken  as  unity.  The  correction  required  to  reduce  to  densities  of  water  free  from  air  are  given 
at  the  foot  of  the  table.  Fdr  all  ordinary  purposes  the  correction  may  be  neglected.  The  temperatures  are  for  the 
hydrogen  thermometer. 


Temp.  C. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

—  0 

0.9998742 

8678 

8613 

8547 

8478 

8408 

8336 

8263 

8188 

8111 

+  o 

0.9998742 

8804 

8864 

8922 

8979 

9035 

9088 

9140 

9191 

9240 

I 

9287 

9332 

9376 

9419 

9460 

9499 

9536 

9572 

9607 

2 

9671 

9701 

9729 

9755 

9780 

9803 

9825 

9846 

9864 

9881 

3 

9897 

9911 

9923 

9934 

9944 

9952 

9958 

9963 

9966 

9968 

4 

9968 

9966 

9964 

9959 

9953 

9946 

9933 

9927 

99*5 

9901 

5 

0.9999886 

9870 

9852 

9833 

9812 

9790 

9766 

9740 

97M 

9685 

6 

9656 

9625 

9592 

9558 

9522 

9485 

9446 

9407 

9365 

9322 

8 

9278 
8758 

9232 
8697 

9185 
8636 

9i37 

8573 

9087 
8509 

9035 
8443 

8982 
8376 

8928 
8308 

8873 
8238 

8815 
8167 

9 

8095 

8021 

7946 

7869 

7791 

7712 

7631 

7549 

7466 

738i 

10 

0.9997295 

7208 

7119 

7029 

6937 

6844 

6750 

6654 

6558 

6459 

ii 

6360 

6259 

6i57 

6053 

5949 

5842 

5735 

5626 

55i6 

5405 

12 

5292 

5178 

5063 

4947 

4829 

4710 

4590 

4468 

4345 

4221 

!3 

4096 

3969 

3841 

3712 

358i 

345° 

33r7 

3182 

3°47 

2910 

14 

2772 

2633 

2493 

235i 

2208 

2064 

1919 

1772 

1624 

1475 

15 

o-999i325 

1174 

IO2I 

0867 

0712 

°556 

°399 

0240 

0080 

9919 

16 

89757 

7594 

9429 

9264 

9097 

8929 

8760 

8589 

8418 

8245 

i? 

8071 

7896 

7720 

7543 

7365 

7185 

7004 

6823 

6640 

6456 

18 

6270 

6084 

5897 

5708 

5518 

5328 

5^6 

4943 

4749 

4553 

19 

4357 

4160 

3961 

3762 

356i 

3359 

3'S7 

2953 

2748 

2542 

20 

21 

0-9982335 

0205 

2126 
9987 

1917 
9767 

1707 
9546 

1496 
9325 

1283 
9102 

1070 

IB 

0640 
8427 

0423 
8200 

22 

77972 

7744 

75H 

7283 

7051 

6818 

6584 

6340 

6114 

5877 

23 

5639 

5400 

5160 

4920 

4678 

4435 

4191 

3947 

3701 

3455 

24 

3207 

2959 

2709 

2459 

2208 

1956 

1702 

1448 

JI93 

0937 

25 

0.9970681 

0423 

0164 

9904 

9644 

938! 

9120 

8857 

8592 

5327 

26 

68061 

7794 

7527 

7258 

6988 

6718 

6447 

6i75 

59oi 

5628 

27 

5353 

5077 

4801 

4523 

4245 

3966 

3686 

3405 

3I24 

2841 

28 

2558 

2274 

1989 

T703 

1416 

1129 

0840 

0551 

0261 

997  1 

29 

59679 

9387 

9094 

8800 

8505 

8209 

8913 

7616 

73i8 

7019 

30 

0.9956720 

6419 

6118 

5816 

55J4 

5210 

4906 

4601 

4296 

3989 

3i 

3682 

3374 

3066 

2756 

2446 

2135 

1823 

IS" 

1198 

0884 

If  we  put  D't  for  the  density  of  water  containing  air  and  Dt  for  the  density  of  water  free 

from  air,  we  get  the  following  corrections  on  the  above  table  to  reduce  to  pure  water  :  — 

t=           0123456789          10 

io7(Dt-D't)  =  25         27        29         31        32         33        33         34        34         33          32 

t=           11        12      13        14       15       16        17        18        19       20  —  32 

io7(Dt-D't)  =  31          29       27          25        22         19         16        12          8           4    negligible. 

*  This  table  is  given  by  Marek  in  •'  Wied.  Ann.,"  vol.  44,  p.  172,  1891. 
SMITHSONIAN  TABLES. 

92 


TABLE  103. 

VOLUME  IN  CUBIC  CENTIMETRES  AT  VARIOUS  TEMPERATURES  OF  A 
CUBIC  CENTIMETRE  OF  WATER  AT  THE  TEMPERATURE  OF  MAXI- 
MUM DENSITY.* 

The  water  in  this  case  is  supposed  to  be  free  from  air.    The  temperatures  are  by  the  hydrogen  thermometer. 


Temp.  C. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

0° 

1.000127 

120 

114 

108 

IO2 

096 

091 

086 

080 

075 

I 

070 

066 

06  1 

057 

052 

048 

044 

040 

037 

033 

2 

030 

027 

024 

02  1 

OI9 

017 

014 

012 

OIO 

009 

3 

007 

006 

004 

003 

OO2 

002 

OOI 

OOI 

000 

ooo 

4 

000 

000 

OOI 

OOI 

OOI 

002 

003 

OO4 

005 

007 

5 

1.000008 

OIO 

012 

014 

016 

018 

020 

023 

026 

029 

6 

032 

035 

038 

041 

045 

049 

053 

057 

06  1 

065 

7 

069 

074 

079 

084 

089 

094 

099 

105 

no 

no 

8 

122 

128 

141 

M7 

*54 

1  60 

I67 

174 

181 

9 

I89 

196 

204 

211 

219 

227 

235 

244 

252 

260 

10 

1.000269 

278 

287 

296 

305 

3H 

324 

334 

343 

353 

n 

363 

373 

383 

394 

405 

426 

437 

448 

459 

12 

471 

482 

494 

505 

517 

529 

54i 

553 

566 

578 

13 

591 

603 

616 

629 

642 

655 

668 

68  1 

695 

709 

736 

75° 

765 

779 

794 

809 

823 

838 

853 

15 

1.000868 

884 

899 

914 

930 

945 

961 

977 

993 

669 

16 

1025 

042 

058 

075 

091 

1  08 

125 

142 

'59 

177 

17 

194 

211 

229 

247 

265 

283 

301 

319 

338 

356 

18 

374 
566 

393 

5«5 

412 
605 

I31 
625 

45° 
645 

469 
666 

488 
686 

5°7 
707 

527 

727 

546 
748 

20 

1.001768 

789 

810 

8ji 

Q  f 

874 

835 

916 

238 

960 

21 

981 

003 

025 

047 

069 

092 

114 

137 

159 

182 

22 

2205 

228 

25r 

274 

297 

320 

343 

367 

39  * 

414 

23 

438 

462 

486 

510 

534 

559 

583 

607 

632 

657 

24 

682 

707 

732 

757 

782 

807 

833 

858 

884 

910 

25 

1.002935 

961 

987 

674 

040 

566 

092 

TTcj 

146 

172 

26 

3T99 

226 

280 

307 

335 

362 

389 

41? 

445 

-7 

472 

500 

528 

556 

584 

612 

641 

669 

697 

726 

28 

754 

783 

812 

841 

870 

899 

928 

957 

987 

016 

29 

4045 

075 

I05 

134 

164 

194 

224 

254 

284 

3T5 

30 

3r 

1.004345 
653 

375 

406 
2i6 

436 

748 

467 

780 

498 
§11 

529. 
843 

560 

§75 

907 

622 

939 

32 

971 

003 

036 

068 

101 

133 

166 

199 

231 

264 

33 
34 

5297 
631 

363 
699 

396 

733 

430 
767 

463 
80  1 

497 
835 

530 
870 

564 
904 

597 
939 

35 

1-005973 

008 

042 

077 

in 

146 

T8T 

217 

212- 

237 

*  The  table  is  quoted  from  Landolt  and  Bernstein's  "  Physikalische  Chemie  Tabellen,"  and  depends  on  experi- 
ments by  Thiesen,  Scheel,  and  Marek. 
SMITHSONIAN   TABLES. 

93 


TABLE  1O4. 


DENSITY   AND   VOLUME   OF  WATER.* 


The  mass  of  one  cubic  centimetre  at  4°  C.  is  taken  as  unity. 


Temp.  C. 

Density. 

Volume. 

Temp.  C. 

Density. 

Volume. 

—  10° 

0.998145 

1.001858 

25° 

0.99712 

1.00289 

g 

8427 

1575 

26 

687 

314 

8 

8685 

13*7 

27 

660 

341 

j 

8911 

1089 

28 

633 

368 

—  6 

9118 

•0883 

29 

605 

396 

—  5 

0.999298 

1.000702 

30 

0.99577 

1.00425 

—  4 

9455 

0545 

31 

547 

455 

—  3 

959° 

0410 

32 

5*7 

480 

—  2 

9703 

0297 

33 

485 

518 

—  I 

9797 

0203 

34 

452 

551 

0 

0.999871 
9928 

1.000129 
0072 

35 

36 

0.99418 
383 

1.00586 
621 

2 

9969 

0031 

37 

347 

657 

3 

9991 

0009 

38 

310 

694 

4 

i  .000000 

0000 

39 

273 

732 

5 

0.999990 

1.  0000  10 

40 

o-99235 

1.00770 

6 

9970 

0030 

41 

197 

809 

7 

9933 

0067 

42 

158 

849 

8 

9886 

0114 

43 

118 

889 

9 

9824 

0176 

44 

078 

929 

10 

0.999747 

1.000253 

45 

0.99037 

1.00971 

ii 

9655 

0345 

46 

8996 

1014 

12 

9549 

045  l 

47 

954 

1057 

13 

943° 

0570 

48 

910 

IIOI 

14 

9299 

0701 

49 

865 

1148 

15 

0.999160 

1.000841 

50 

0.98820 

1.01195 

16 

9002 
8841 

0999 

1160 

11 

582 
338 

439 
691 

18 
19 

8654 
8460 

1348 
1542 

65 

70 

074 
7794 

964 
256 

20 

0.998259 

1.001744 

75 

0.97498 

1.01566 

21 

8047 

'957 

So 

194 

887 

22 

7826 

2177 

85 

6879 

221 

23 

7601 

2405 

90 

556 

567 

24 

7367 

2641 

95 

219 

931 

25 

0.997120 

1.002888 

100 

0.95865 

I.023I2 

SMITHSONIAN  TABLES. 


Rossetti,  "  Berl.  Ber."  1867. 


94 


TABLE  1O5. 


DENSITY   OF    MERCURY. 


Density  or  mass  in  grammes  per  cubic  centimetre,  and  the  volume  in  cubic  centimetres  of  one  gramme 
of  mercury.  The  density  at  o°  is  taken  as  13.5956,*  and  the  volume  at  temperature  t  is  Vt  = 
V0  (i  +  .000181792*+  175  X  ID-"/*  -f  35  u6  x  10^/3)  f 


Temp.  C. 

Mass  in 
grammes  per 
cub.  cm. 

Volume  of 
i  gramme  in 
cub-  cms. 

Temp.  C. 

Mass  in 
grammes  per 
cub.  cm. 

Volume  of 
j  gramme  in 
cub.  cms. 

—  10° 

-I 

13.6203 
6178 
6153 

0.0734195 

4329 
4463 

30° 

31 
32 

13.5218 
5^9 

0-0739544 
9678 
9812 

—  6 

6129 
6104 

4596 
4730 

33 

34 

SMS 

5120 

9945 
40079 

—  5 

13.6079 

0.0734864 

35 

13.5096 

0.0740213 

4 

6°55 

4997 

36 

0346 

—  3 

6030 

5131 

5°47 

0480 

—  2 

6005 

5265 

38 

5022 

0614 

—  I 

598i 

5398 

39 

4998 

0748 

0 

1  3-  5956 

0-0735532 

40 

1  34974 

0.6740882 

I 

593  * 

5666 

5° 

4731 

2221 

2 

5907 

5800 

60 

4488 

356l 

3 

5882 

5933 

70 

4246 

4901 

4 

5857 

6067 

80 

4005 

6243 

5 

13-5833 

0.0736201 

90 

I3-3764 

0.0747586 

6 

7 

5783 

6334 
6468 

IOO 
IIO 

35J4 
3284 

8931 
50276 

8 

5759 

6602 

120 

3045 

1624 

9 

5734 

6736 

130 

2807 

2974 

10 

I3-5709 

0.0736869 

140 

13.2569 

0.0754325 

ii 

5685 

7003 

I5° 

2331 

5679 

12 

5660 

7137 

1  60 

2094 

7°35 

'3 

5635 

7270 

170 

1858 

/    U  J 

8394 

H 

5611 

7404 

180 

1621 

9755 

15 

I3-5586 

0-0737538 

190 

I3-I385 

0.0761  1  20 

16 

5562 

7672 

200 

1150 

2486 

17 

5537 

7805 

2IO 

0915 

3854 

18 

5513 

7939 

22O 

0680 

5230 

19 

5488 

8073 

230 

0445 

6667 

20 

I3-5463 

0.0738207 

240 

13.0210 

0.0767988 

21 

5439 

8340 

250 

12.9976 

9372 

22 

54M 

8474 

260 

9742 

70760 

23 

5390 

8608 

270 

9508 

1252 

24 

5365 

8742 

280 

9274 

3549 

25 

I3-534I 

0.0738875 

290 

12.9041 

0-0774950 

26 

53*6 

9009 

300 

8807 

6355 

27 

5292 

9M3 

310 

8573 

7765 

28 

5267 

3277 

320 

8340 

9180 

29 

5243 

9-411 

330 

8107 

80600 

30 

13.5218 

0-0739544 

340 

12.7873 

0.0782025 

35° 

7640 

3455 

36o 

7406 

4891 

*  Marek,  "  Trav.  et  Me*m.  du  Bur.  Int.  des  Poids  et  Me"s."  2,  1883. 
t  Broch,  1.  c. 

SMITHSONIAN  TABLES. 

95 


TABLE  106. 

SPECIFIC   GRAVITY   OF   AQUEOUS   ETHYL   ALCOHOL, 


(a)  The  numbers  here  tabulated  are  the  specific  gravities  at  60°  F.,  in  terms  of 
ture,  of  water  containing  the  percentages  by  weight  of  alcohol  of  specific  gravi 
same  temperatures.* 

water  at 
ty  .7938,  w 

the  same  tempera- 

Percentage 
of  alcohol 
by  weight. 

0 

1 

2 

3 

4 

5 

6 

7 

8               9 

Specific  gravity  at  15°.  56  C.  in  terms  of  water  at  the  same  temperature. 

0 

10 
20 

30 
40 

50 

60 
70 
80 
90 

1.  0000 

.9841 
.9716 

•9578 
•9396 

0.9184 

.8956 

.8721 
.8483 
.8228 

.9828 

•9703 
.9560 
•9376 

.9160 
•8932 
.8696 

.8459 
.8199 

•9965 
•9815 
.9691 

•9544 
•9356 

•9135 
.8908 
.8672 

.8434 
.8172 

.9678 
.9528 
•9335 

•9"3 

.8886 
.8649 
.8408 
.8145 

•9930 
•9789 
.9665 

•95" 
•93H 

.9090 
.8863 
.8625 
.8382 
.8118 

.9914 

.9778 
.9652 
.9490 
.9292 

.9069 

.8840 
.8603 

'.8089 

.9898 
.9766 
•9638 
•9470 
.9270 

.9047 
.8816 
.8581 

•8331 
.8061 

.9884 
•9753 
•9623 
.9452 
.9249 

.9025 
.8793 
•8557 
.8305 
•8031 

.9869       .9855 
.9741        .9728 
•9609       .9593 
.9434       .9416 
.9228       .9206 

.9001        .8979 
•8769       .8745 
.8533       -8508 
.8279       .8254 
.8001        .7969 

(b)  The  following  are  the  values  adopted  by  the  "  Kaiserlichen  Normal-Aichungs  Kommission."    They  are 
based  on  Mendelejeff's  formula,!  and  are  for  alcohol  of  specific  gravity  .79425,  at  15  D  C.,  in  terms  of  water 
at  15°  C.  ;  temperatures  measured  by  the  hydrogen  thermometer. 

a  •IS 

4)   o   4> 

£13  * 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

Specific  gravity  at  15°  C.  in  terms  of  water  at  the  same  temperature. 

0 

10 

20 
30 
40 

50 

60 
70 
80 
90 

1.  00000 

•98393 
.97164 
•95770 

•93973 

0.91865 
89604 
87265 
84852 
82304 

.99812 
.98262 
.97040 
.95608 
•93773 

.91644 

•89373 
.87028 
.84606 
.82036 

.99630 

•98135 
.96913 

•95443 
•93570 

.91421 
.89141 
.86789 
.84358 
.81763 

.98010 
.96783 
•95273 
•93365 

.91197 
.88909 
.86550 
.84108 
.81488 

.99284 
.97888 
.96650 
•95099 
•93J57 

.90972 
.88676 
.86310 

•83857 
.81207 

.99120 
.97768 

•9651  3 
.94920 
.92947 

.90746 
.88443 
.86070 
.83604 
.80923 

•98963 
.97648 

•96373 
•94738 
.92734 

.90519 
.88208 
.85828 

.83349 
.80634 

.98812 

.97528 
.96228 

•94552 
.92519 

.90292 
.87974 
.85586 
.83091 
•80339 

.98667 
.97408 
.96080 

•94363 
.92303 

.90063 
.87738 
•85342 
.82832 
.80040 

.98528 
.97287 

•95927 
.94169 
.92088 

.89834 
.87502 
.85098 
.82569 
•79735 

(c)  The  following  values  have  the  same  authority  as  the  last  ;  the  percentage  of  alcohol  being  given  by  volume 
instead  of  by  weight,  and  the  temperature  15°.  56  C.  on  the  mercury  in  Thuringian  glass  thermometer  ;  the 
specific  gravity  of  the  absolute  alcohol  being  .79391. 

Percentage 
of  alcohol 
by  volume. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Specific  gravity  at  i5°.s6  C.  in  terms  of  water  at  same  temperati 

re. 

0 

10 

20 
30 
40 

50 

60 
70 
80 
90 

I  .OOOOO 

•98657 
.97608 
.96541 

•95'85 

0-93445 
•91358 
.89010 

•86395 
.83400 

.99847 
•98543 
•97507 
.96421 
.95029 

•93250 
•9TI34 
.88762 
.86116 
•83065 

.99699 
.98432 
.97405 
.96298 
.94868 

•93052 
.90907 
.88511 

•85833 
.82721 

•99555 
.98324 
.97304 
.96172 
.94704 

.92850 
.90678 
.88257 
•85547 
.82365 

•99415 
.98218 
.97201 
•96043 
•94536 

.92646 
.90447 
.88000 
.85256 
.81997 

.99279 
.98114 
97097 
.95910 
•94364 

•92439 
.90214 
.87740 
.84961 
.81616 

.99147 
.98011 
.96991 

•95773 
.94188 

.92229 
.89978 

•87477 
.84660 
.81217 

.90019 
.97909 
.96883 
•95632 
.94008 

.92015 
.89740 
.87211 

•84355 
.80800 

.98895 
.97808 
.96772 

•95487 
.93824 

.91799 
.89499 
.86943 
.84044 
.80359 

.98774 
.97708 
.96658 
•95338 
.93636 

.91580 
.89256 
.86670 
.83726 
.79891 

*  Fownes,  "  Phil.  Trans.  Roy.  Soc."  1847. 
t  "  Pogg.  Ann."  vol.  138,  1869. 


SMITHSONIAN  TABLES. 


96 


DENSITY  OF  AQUEOUS  METHYL  ALCOHOL.' 


TABLE   1O7. 


Densities  of  aqueous  methyl  alcohol  at  o°  and  15.56  C.,  water  at  4°  C.  being  taken  as  looooo.  The  numbers  in  the 
columns  a  and  b  are  the  coefficients  in  the  equation  p«  =  p0  —  at  —  bP  where  p«  is  the  density  at  temperature  /. 
This  equation  may  be  taken  to  hold  between  o^  and  20°  C. 


Percent- 

Density 

Density 

Percent- 

Density 

Density 

age  of 

at 

at 

a 

b 

age  of 

at 

at 

a 

CH4O. 

o°C. 

iS°.56C. 

CH40. 

o°C. 

1  5°-  56  C. 

0 

I 

99987 
99806 

99907 
99729 

—  6.0 
—  5-4 

0.705 
•694 

50 

92873 
92691 

91661 

65.41 
66.19 

2 

99631 

99554 

-4.8 

.681 

52 

92507 

66.95 

3 

99462 

99382 

—  3-9 

.670 

53 

92320 

91267 

67.68 

4 

99299 

99214 

'659 

54 

92130 

91066 

68.39 

5 

99142 

99048 

—  2.2 

0.648 

55 

9*938 

90863 

69.07 

6 

98990 

98893 

—  1.2 

•634 

56 

9*742 

90657 

69.72 

I 

98843 
98701 

98726 
98569 

—  O.2 
+  0.9 

.621 
.609 

% 

9*544 
9*343 

90450 
90239 

70.35 
70.96 

9 

98563 

98414 

2.1 

.596 

59 

9**  39 

90026 

7*-54 

10 

ii 

98429 
98299 

98262 
98111 

{I 

0.581 
.569 

60 

61 

909*7 
90706 

89798 
89580 

71.96 

72-37 

12 

98171 

97962 

6.2 

•552 

62 

90492 

89358 

72.91 

13 

98048 

97814 

7-8 

•536 

63 

90276 

89*33 

73-45 

14 

97926 

97668 

9-5 

•5J9 

64 

90056 

88905 

73-98 

15 

97806 

97523 

II.O 

0.500 

65 

89835 

88676 

74-51 

16 

97689 

97379 

12.5 

.480 

66 

89611 

88443 

75-05 

17 

97573 

97235 

14.5 

.461 

67 

89384 

88208 

75-57 

18 

97459 

97093 

16.2 

.440 

68 

89*54 

87970 

76.10 

J9 

97346 

96950 

18.3 

.420 

69 

88922 

87714 

76.62 

20 

97233 

96808 

20.0 

0.398 

70 

88687 

87487 

77-14 

21 

97120 

96666 

22.2 

•373 

71 

88470 

87262 

77.66 

22 
23 

97007 
96894 

96524 
96381 

24-3 
26.4 

•350 
.321 

72 
73 

88237 
88003 

87021 
86779 

78.18 
78.69 

24 

96780 

96238 

29.0 

.291 

74 

87767 

86535 

79.20 

25 

96665 

96093 

3r-3 

0.261 

75 

87530 

86290 

79.71 

26 

28 

96549 
96430 
96310 

95949 
95802 

95655 

33-8 
36.0 
38.8 

.230 
.191 

76 

87290 
87049 
86806 

86042 

85793 

85542 

80.22 
80.72 
81.23 

29 

96187 

95506 

41.1 

.106 

79 

86561 

85290 

8i.73 

Equation  pt  =  Po  —  at 

80 

86314 

85035 

82.22 

81 

86066 

8477Q 

82.72 

30 

96057 

95367 
95211 

44-36 
45-66 

82 
83 

85816 
85564 

TV  /  S 

84521 
84262 

/ 

83.21 
83.70 

32 

95783 

95053 

46.93 

84 

853*o 

84001 

84.19 

33 
34 

95643 
95500 

94894 
94732 

48.17 
49-39 

85 

86 

85055 
84798 

83738 
83473 

84.67 
85.16 

35 

95354 

94567 

50.58 

87 

84539 

83207 

85.64 

8s 

36 
37 

95204 
95°5r 

94399 
94228 

5*-75 
52.89 

o3 
3 

88 
89 

84278 
84015 

82938 
82668 

6.12 

86.59 

38 
39 

94895 
94734 

94055 
93877 

54.01 

I 

90 

9* 

8375* 
83485 

82396 
82123 

87.07 

87-54 

40 

42 

94571 
94400 

94239 

93697 
93335 

56-16 
57-20 
58.22 

* 

92 
93 
94 

83218 
82948 
82677 

81849 
81572 
81293 

88.01 
88.48 
88.94 

43 
44 

94076 
939" 

93*55 
92975 

59-20 
60.17 

1 

95 

96 

82404 
82129 

81013 
80731 

89.40 
89.86 

45 

46 
47 

93744 
93575 
93403 

92793 
92610 
92424 

61.10 
62.01 
62.90 

97 
98 

99 

81853 
81576 
81295 

80448 
80164 
79872 

90.32 
90.78 
9*-23 

48 
49 

93229 
93052 

92237 
92047 

64.60 

100 

81015 

79589 

91.68 

*  Quoted  from  the  results  of  Dittmar  &  Fawsitt, 
SMITHSONIAN  TABLES. 

97 


'  Trans.  Roy.  Soc.  Edin."  vol.  33. 


TABLE  1O8. 


VARIATION    OF   THE    DENSITY   OF   ALCOHOL    WITH    TEMPERATURE 


(a)  The  density  of  alcohol  at  t°  in  terms  of  water  at  4°  is  given  *  by  the  following  equation  : 

dt  =1  0.80025  —  0.0008340*  —  000000  29^. 

From  this  formula  the 

following  table  has  been  calculated. 

U 

ci. 

Density  or  Mass  in  grammes  per  cubic  centimetre. 

| 
H             0 

1 

2 

3 

4 

5 

6               7 

8 

9 

0       .80625 
10      .79788 

20         .78945 
30         .78097 

-80541 
.79704 
.78860 
.78012 

.80457 
.79620 
•78775 
•77927 

.80374 

•79535 
.78691 
.77841 

.80290 

•79451 
.78606 

•77756 

.80207 

.79367 
.78522 
.77671 

.80123      .80039 
.79283      -79198 
.78437      -78352 
77585      .77500 

•79956 
.79114 
.78267 
•77414 

.79872 
.79029 
.78182 
.77329 

(b)  Variations  with  temperature  of  the  density  of  water  containing  different  percentages  of  alcohol.     Water 
at  4°  C.  is  taken  as  unity.  t 

Percent- 
age of 
alcohol  by 
weight. 

Density  at  temp.  C. 

Percent- 
age of 
alcohol  by 
weight. 

Density  at  temp.  C. 

0° 

10 

o    • 

20° 

30° 

0° 

10° 

20° 

'   30° 

0 

5 

10 

15 

20 

0.99988 

•99r35 
.98493 

•97995 
.97566 

0-99975 
•99I][3 
.98409 
.97816 
.97263 

0.99831 
•98945 

0-99579 
.98680 
.97892 
.97142 
.96413 

50 

65 
70 

0.92940 
.91848 

f595 
420 

0.92182 

.91074 
.89944 

.88790 
.87613 

0.91400 
.90275 
.89129 
.97961 
.86781 

0.90577 
.89456 
.88304 
.87125 
.85925 

25 

30 
35 
40 
45 

0.97115 
.96540 
.95784 
•94939 
•93977 

0.96672 
•95998 
•95*74 
.94255 
.93254 

0.96185 
•95403 

•945T4 
•93511 
.92493 

0.95628 
-947  5  i 

.92787 
.91710 

75 

80 

85 
90 

95 

0.87245 
.86035 
.84789 
.83482 
.82119 

0.86427 

.85215 
.83967 
.82665 

.81291 

0.85580 
.84366 

.83"5 
.81801 

•80433 

0.84719 

•83483 
.82232 
.80918 
•79553 

50 

0.92940 

0.92182 

0.91400 

0.90577 

100 

0.80625 

0.79788 

0.78945 

0.78096 

*  Mendelejeff,  "  Pogg.  Ann."  vol.  138. 

t  Quoted  from  Landolt  and  Bornstein,  "  Phys.  Che 


Tab."  p.  223. 


SMITHSONIAN  TABLES. 


98 


TABLE  109. 


VELOCITY   OF   SOUND   IN    AIR. 


Rowland  has  discussed  (Proc.  Am.  Acad.  vol.  15,  p.  144)  the  principal  determination  of  the  velocity  of  sound  in 
atmospheric  air.  The  following  table,  together  with  the  footnotes  and  references,  are  quoted  from  his  paper. 
Some  later  determinations  will  be  found  in  Table  in,  on  the  velocity  of  sound  in  gases. 


i? 

j 

1, 

1 

T3 

> 

ll 

M 

*** 

"MC 

«1 

-c_o 

'1 

*°  w 

II 

1 

>, 

m 

^^ 

g-e 
frl 

bit 

|| 

s  £ 

J3>* 

1 

1 

11 

1 

i 

>  o 

li 

'G^1  -^, 

J* 

I 

1738 

France   .     . 

_ 

5°-7°-5  C. 

172.56  T. 

332.9m. 

332.6m. 

2 

2 

1811 

DUsseldorf 

40 

333-7  b 

— 

332.7 

2 

3 

4 

5 

1821 

1822 
1822 

India.     .    | 

France   .     . 
Austria  .     . 

120 

70 

83°-95  F. 
79°-9  F. 
i5°.9C. 
9°.4  C. 

1  1  49.  2  ft. 
I  I3I.5  ft. 

340.89  m. 

333-oc 
329.6  c 
33I-36 
332.96 

:[ 

330.9 
330-8 
332-5, 

I 

6 

1823 

Holland     j 

22  shots 
I4       " 

ii°'.oC*.« 

340-37 
339-27 

333-62 
332.62 

332.82* 
33i.9i* 

: 

7 

8 

1824-5 
1839 

Port  Bowen 

51 

-38°  F.  to  +33°  F. 
5°.  5  to  9°  C. 

336.50 

332-27/ 
332.20? 

332-0 

J 

9 

1844 

Alps  .     .     . 

34 

8°.  17  C. 

338.01 

332-11 

332.37 

— 

4 

IO 

1868* 

France   .     . 

149 

2°  to  20°  C. 

33o-7i 

10 

General  mean  deduced  by  Rowland,  331.75. 

Correcting  for  the  normal  carbonic  acid  in  the  atmosphere,  this  becomes  331.78  metres 
per  second  in  pure  dry  air  at  o°  C. 


REFERENCES. 

1  French  Academy  :  "  Mem.  de  1'Acad.  des  Sci."  1738,  p.  128. 

2  Benzenburg  :  Gibberts's  "  Annalen,"  vol.  42,  p.  i. 

3  Goldingham  :  "  Phil.  Trans."  1823,  p.  96. 

4  Bureau  of  Longitude  :  "  Ann.  de  Chim."  1822,  vol.  20,  p.  210;   also, "  CEuvres  d'Arago," 

"  Mem.  Sci."  ii.  i. 

5  Stampfer  und  Von  Myrbach :  "  Pogg.  Ann."  vol.  5,  p.  496. 

6  Moll  and  Van  Beek  :  "  Phil.  Trans."  1824,  p.  424- 

7  Parry  and  Foster :  "  Journal  of  the  Third  Voyage,"  1824-5,  App.  p.  86 ;  "  Phil.  Trans." 

1828,  p.  97. 

8  Savant :  "  Ann.  de  Chim."  ser.  2,  vol.  71,  p.  20.     Recalculated. 

9  Bravais  and  Martins  :  "  Ann.  de  Chim."  ser.  3,  vol.  13,  p.  5. 
10  Regnault:  "  Rel.  des  Exp."  iii.  p.  533- 


a  I  believe  that  I  calculated  these  reduced  numbers  on  the  supposition  that  the  air  was  rather  more  than 
half  saturated  with  moisture. 

b  Reduced  to  o°  C.  by  empirical  formula. 

c  Wind  calm. 

d  Moll  and  Van  Beek  found  332.049  at  o°  C.  for  dry  air.    They  used  the  coefficient  .00375  to 
take  the  numbers  as  recalculated  by  Schroder  van  der  Kolk. 

e  An  error  of  0.21°  C.  was  made  in  the  original.     See  Schroder  van  der  Kolk,     Phil.  Mag.     1865. 

/  Corrected  for  wind  by  Galbraith. 

g  Recalculated  from  Savart's  results. 


*  This  is  given  as  1864  in  Rowland's  table.     The  original  paper  is  in  "  Mem.  de  1'Institut,"  vol.  37,  1868. 
SMITHSONIAN  TABLES. 

99 


TABLE  11 0, 


VELOCITY  OF  SOUND  IN  SOLIDS, 


The  numbers  given  in  this  table  refer  to  the  velocity  of  sound  along  a  bar  of  the  substance,  and  hence  depend  on  th» 
Young's  Modulus  of  elasticity  of  the  material.  The  elastic  constants  of  most  of  the  materials  given  in  this  table 
vary  through  a  somewhat  wide  range,  and  hence  the  numbers  can  only  be  taken  as  rough  approximations  to  the 
velocity  which  may  be  obtained  in  any  particular  case.  When  temperatures  are  not  marked,  between  10°  and  20° 
is  to  be  understood. 


Substance. 

Temp.  C. 

o 

Velocity  in 
metres  per 
second. 

Velocity  in 
feet  per 
second. 

Authority. 

Metals  :  Aluminium     . 

_ 

5I04 

16740 

Masson. 

Brass      .... 

- 

35°° 

11480 

Various. 

Cadmium 

- 

2307 

7570 

Masson. 

Cobalt    .        .        .        . 

— 

4724 

JS5°° 

a 

Copper  .        »        •        • 

2O 

35°° 

11670 

Wertheim. 

" 

100 

3290 

10800 

a 

« 

2OO 

2950 

9690 

u 

Gold  (soft)     !        '.        '. 

2O 

i?43 

57i7 

" 

"          .... 

100 

1720 

5640 

it 

« 

200 

*735 

569i 

u 

Gold  (hard)    . 

- 

2IOO 

6890 

Various. 

Iron  and  soft  steel 

— 

5000 

16410 

" 

Iron        .        .        .        . 

2O 

5*30 

16820 

Wertheim. 

"           .... 

IOO 

53°o 

J7390 

" 

« 

2OO 

4720 

15480 

u 

"  cast  steel 

2O 

4990 

16360 

U 

«      «      « 

IOO 

4920 

16150 

« 

"      "      "     .        .        . 

200 

4790 

15710 

" 

Magnesium    .        .        . 

- 

4602 

15100 

Melde. 

Nickel    .... 

— 

4973 

16320 

Masson. 

Palladium       .        ... 

_ 

3IS° 

10340 

Various. 

Platinum 

20 

2690 

8815 

Wertheim. 

« 

IOO 

2570 

8437 

" 

"                     ... 

2OO 

2460 

8079 

" 

Silver                              * 

20 

2610 

8553 

« 

M 

IOO 

2640 

8658 

« 

It 

2OO 

2480 

8127 

" 

Tin         '.'.!! 

- 

2500 

8200 

Various. 

Zinc        .... 

— 

3700 

12140 

" 

Various  :  Brick    . 

_ 

3652 

11980 

Chladni. 

Clay  rock     .         .        >    ; 

- 

3480 

11420 

Gray  &  Milne. 

Granite          .         . 

— 

395° 

12960 

" 

Marble 

- 

3810 

12500 

" 

Slate     .        .        .        .    ' 

— 

45Jo 

14800 

" 

Tuff      .... 

— 

2850 

9350 

u 

Class                       i  from 

- 

5000 

16410 

Various. 

I       to 

— 

6000 

19690 

" 

Ivory    .... 

- 

3OI3 

9886 

Ciccone  &  Campanile. 

Vulcanized  rubber          ( 

O 

54 

i/7 

Exner. 

(black)  J 

5° 

31 

102 

" 

«     (red)   . 

o 

69 

226 

« 

"          u 

70 

34 

III 

" 

Woods  :  Ash,  along  the  fibre      . 

4670 

I53IO 

Wertheim. 

"     across  the  rings    . 

— 

1390 

4570 

" 

"     along  the  rings 

— 

1260 

4140 

" 

Beech,  along  the  fibre  . 

- 

3340 

10960 

" 

"       across  the  rings 

— 

1840 

6030 

it 

"       along  the  rings 

_ 

1415 

4640 

H 

Elm,  along  the  fibre 

_ 

4120 

J35l6 

U 

"      across  the  rings    . 

- 

1420 

4665 

" 

"      along  the  rings     . 

— 

1013 

3324 

U 

Fir,  along  the  fibre 

- 

4640 

15220 

« 

Maple          " 

— 

4110 

13470 

U 

Oak             " 

— 

3850 

12620 

(( 

Pine             " 

— 

3320 

10900 

<« 

Poplar 

_ 

4280 

14050 

« 

Sycamore    " 

" 

4460 

14640 

SMITHSONIAN  TABLES. 


IOO 


TABLE  111 


VELOCITY  OF  SOUND  IN  LIQUIDS  AND  CASES, 


Substance. 

1 
Temp.  C. 

o 

Velocity  in 
metres  per 
second. 

Velocity  in 
feet  per 
second. 

Authority. 

Liquids:  Alcohol     .... 

8.4 

1264 

4148 

Martini. 

"           .... 

23 

1160 

3806 

Wertheim. 

Ether         .... 

O 

"59 

3803 

" 

Oil  of  turpentine 
Water  (  Lake  Geneva) 

24 

9 

1212 

T435 

3977 
4708 

Colladon  &  Sturm. 

"       (from  Seine  river) 

15 

H37 

47H 

Wertheim. 

«<           «         «          « 

3° 

1528 

5OI3 

" 

"           "         "          " 

60 

1724 

5657 

" 

Water        .        .        .        . 

3-9 

4591 

Martini. 

"            .... 

13.7 

J437 

47H 

" 

"            .... 

25.2 

1457 

478o 

M 

o 

OQ2 

Dulong. 

0 

33  r  -6 

.7 

087 

Wertheim. 

« 

o 

777 

092 

Masson. 

« 

o 

333 

7  TO.  7 

085 

Le  Roux. 

t( 

o 

33      / 

089 

Schneebeli. 

u 

o 

332-5 

Kayser. 

« 

o 

080 

Wullner. 

M 

o 

771.7 

088 

Blaikley. 

4< 

o 

33      1 

1086 

Violle  &  Vautier. 

u 

—  10.9 

326.1 

1070 

Greely. 

44 

—  2C.7 

717.1 

1040 

M 

M 

-37-8 

3    / 

709.7 

1016 

« 

a 

-45-6 

s 

70S  -6 

1002 

« 

<« 

*TJ 

O 

3     J 

332-4 

1091 

Stone. 

Ammonia     .        .        .        • 

O 

1361 

Masson. 

Carbon  monoxide 

o 

337-1 

1106 

Wullner. 

"      dioxide    .        .        . 

0 
0 

337-4 
261.6 

1107 
858 

Dulong. 

« 

Carbon  disulphide 
Chlorine       . 

o 
o 

189 
206.4 

606 
677 

Masson. 
Martini. 

o 

205-3 

674 

Strecker. 

Ethylene 

0 

3H 

1030 

Dulong. 

Hydrogen     .... 

0 
0 

1269.5 
1286.4 

4165 
4221 

Zoch. 

Illuminating  gas  . 
Methane       .... 

o 
o 

490.4 
422 

1609 

Masson. 

Nitric  oxide 
Nitrous  oxide 

0 
0 

26?.8 

859 

Dulong. 

Oxygen         .... 
Vapors  :  Alcohol      .... 
Ether         .... 

o 
o 

0 

317.2 
230.6 
179.2 

1041 
756 

588 

Masson. 

Water        .... 

0 

401 

1315 

96 

410 

1345 

SMITHSONIAN  TABLES. 


101 


TABLE  112. 
FORCE  OF  GRAVITY  FOR  SEA  LEVEL  AND  DIFFERENT  LATITUDES, 

This  table  has  been  calculated  from  the  formula  g^  =£"45  [r  —  .002662  cos2<£],*  where  <f>  is  the  latitude. 


Lati- 
tude 0. 

ff 

in  cms.  per 
sec.  per  sec. 

Log. 

ff 

in  inches  per 
sec.  per  sec. 

Log. 

ff 

in  feet  per 
sec.  per  sec. 

Log. 

0° 

977.989 

2.990334 

385-034 

2.585498 

32.0862 

1.506318 

5 

8.029 

0352 

.050 

5517 

.0875 

6336 

10 

.147 

0404 

.096 

5570 

.0916 

6388 

15 

•339 

0490 

•173 

5655 

.0977 

6474 

20 

.600 

0605 

•275 

5771 

.1062 

6590 

25 

978.922 

2.990748 

385.402 

2.585914 

32.1168 

1.506732 

30 

9-295 

0913 

.548 

6079 

.1290 

6898 

31 

•374 

0949 

.580 

6114 

.1316 

6933 

32 

•456 

0985 

.612 

6150 

•1343 

6969 

33 

•538 

IO2I 

.644 

6187 

•1370 

7005 

34 

979.622 

2.991059 

385.677 

2.586224 

32.1398 

I-507043 

35 

.707 

1096 

.711 

6262 

•1425 

7080 

36 

•793 

"35 

•745 

6300 

.1454 

7119 

37 

.880 

"73 

•779 

6339 

.1490 

7167 

38 

.968 

1212 

.813 

6377 

•15" 

7196 

39 

980.057 

2.991251 

385-849 

2.586417 

32.1540 

1.507236 

40 

.147 

1291 

.884 

6457 

•1570 

7275 

•237 

1331 

.919 

6496 

.1607 

7325 

42 

•327 

1372 

•955 

6537 

.1630 

7356 

43 

.418 

I4II 

•990 

6577 

.1659 

7395 

44 

980.509 

2.991452 

386.026 

2.586617 

32.1688 

I-507436 

45 

.600 

1492 

.062 

6657 

.1719 

7476 

46 

.691 

*532 

.098 

6698 

.1748 

7516 

47 

.782 

J573 

•134 

6738 

.1778 

7557 

48 

-873 

1613 

.170 

6778 

.1808 

7597 

49 

980.963 

2.991653 

386.205 

2.586818 

32.1838 

1-507637 

5° 

1-053 

1693 

.241 

6858 

.1867 

7677 

51 

•143 

•  1732 

.276 

6898 

.1896 

7716 

52 

.231 

1772 

•3" 

6937 

.1924 

7756 

53 

-318 

1810 

•345 

6975 

7794 

54 

981.407 

2.991849 

386.380 

2.587014 

32-1983 

1-507833 

55 

•493 

1887 

.414 

7053 

.2011 

7871 

56 

57 

£ 

1925 
1962 

•447 
.480 

7090 
7127 

•2039 
.2067 

7909 
7946 

58 

•744 

1998 

•513 

7164 

.2094 

7983 

59 

981.825 

2.992034 

386.545 

2.587200 

32.2121 

1.508018 

60 

•905 

2070 

•576 

7235 

•2147 

8054 

65 

2.278 

2234 

•723 

7400 

.2276 

8229 

70 
75 

.600 
.861 

2377 
2492 

•849 
•952 

7542 
7657 

•2375 
.2460 

8361 
8476 

80 

983-053 

2.992577 

387.028 

2.587742 

32-2523 

1.508561 

85 

.171 

2629 

.074 

7794 

.2562 

8613 

90 

.210 

2646 

.090 

7812 

•2575 

8631 

*  The  constant  .002662  is  based  on  data  given  by  Harkness  (Solar  Parallax  and  Related  Constants,  Washington 
1891). 

The  force  of  gravity  for  any  latitude  <f>  and  elevation  above  sea  level  h  is  very  nearly  expressed  by  the  equation 

J^=jr«(i  —  -002662  cos 20)  [i—  ^(i  — 
where  R  is  the  earth's  radius,  5  the  density  of  the  surface  strata,  and  A  the  mean  density  of  the  earth.     When  S  = 
we  get  the  formula  for  elevation  in  air.     For  ordinary  elevations  on  land      is  nearly  £,  which  gives  for  the  correction 
at  latitude  45°  for  elevated  portions  of  the  earth's  surface 

=  1225.75  A  in  dynes. 

—  386.062  X  -5^  =  482.562  A  in  inch  pound  units. 
4.TC  R 

=  32.1719  X  -5^  =  40-2 149  A  inpoundals. 

This  gives  per  100  feet  elevation  a  correction  of 

.00588  dynes  ) 

.00232  inch  pound  units'  diminution. 
Tooiq-  .x>undals  ) 


GRAVITY. 


TABLE  113. 


In  this  table  the  results  of  a  number  of  the  more  recent  gravity  determinations  are  brought  together.  They  serve  to 
show  the  degree  of  accuracy  which  may  be  assumed  for  the  numbers  in  Table  112.  In  general,  gravity  is  a  little 
lower  than  the  calculated  value  for  stations  far  inland  and  slightly  higher  on  the  coast  line. 


Place. 

Latitude. 

N.  -f,  S.  —  . 

Elevation 
in  metres. 

Gravity  in  dynes. 

Refer- 
ence. 

Observed. 

Reduced  to 
sea  level. 

Singapore 

'°  '2' 

-7     56 
—  8    49 

—  10      00 

13  04 

—  15    55 
—  15    57 
20    43 
20     52 

20      56 
21       18 

32      23 

-33    5| 
—  33    56 
35    4i 
—  36    52 
37     20 
37     20 
37    47 
37    47 
38    53 
39    54 
39    58 
40    27 
40    28 
40    44 
40    46 
41     49 
42    49 

45    31 
46    12 

46      12 

46    57 
47     23 
48     50 
51     28 

52    3° 
54    34 
55     59 
56    28 

57    03 
57    07 
58     18 
59    I0 
59    32 

14 

681 
46 

2 

18 

10 

533 
3001 

3 
117 

3 

2 

43 
ii 
6 

43 
1282 
1282 
114 
114 

10 

1645 

122 
65I 
348 
II 
1288 
I65 

45° 

100 

405 
405 

& 

67 
7 

1 

o 
8 

12 

5 
5 
4 

978.07 
978.24 
978.08 
978.14 
978.36 
978.16 
978.66 
978.52 
978.27 
978.85 
978.90 
978.96 

979-75 
979.67 
979.61 

979-94 
979.67 
979.64 
979-68 

979-95 
980.02 
980.10 
979.68 
980.12 
980.08 
980.09 
980.26 
979.82 
980.34 
980.34 
980.73 
980.58 
980.60 
980.61 
980.67 
980.96 
981.20 
981.26 
981.45 
981.49 
981.59 
981.68 
981.66 

981-73 
981.81 
981.82 

978.07 
978.24 
978.21 
978.15 
978.36 
978.16 
978.66 
978.58 
978.84 
978.85 
978.92 
978.96 

979-75 
979.68 
979.61 

979-94 
979.68 
979.89 
979.92 

979-97 
980.04 
980.10 
979.98 
980.14 
980.20 
980.15 
980.26 
980.05 

9fo.37 
980.42 
980.75 
980.64 
980.66 
980.69 
980.74 
980.97 
981.20 
981.27 
981-45 
981.49 
981.59 
981.68 
981.66 

981-73 
981.81 
981.82 

2 
2 
2 

3 
2 
2 

2 
3 

3 
3 
3 

2 
I 
2 
I 
I 

4 

5 
4 
5 
4 

6 
6 

4 
5 
5 
7 

85 
9 
9 

§ 

8 
8 
4 
4 
4 
4 
^ 
4 
4 
4 

Georgetown,  Ascension    .... 
Green  Mountain,  Ascension  . 
Loanda,  Angola  
Caroline  Islands  

Bridgetown,  Barbadoes     .... 
Jamestown,  St.  Helena     .... 
Longwood,             "             .... 
Pakaoao,  Sandwich  Islands.     .     . 
Lahaina,           "               "... 
j     Haiki,               "               "... 
Honolulu,         '•               "... 
St.  Georges,  Bermuda      .... 

Cape  Town      

Xokio  Japan 

Auckland,  New  Zealand   .... 
Mount  Hamilton,  Cal.  (Lick  Obs.) 

San  Francisco  Cal 

Washington,  D.  C.*     
Denver  Colo.  .               

York   Pa 

Allegheny   Pa  •     • 

Hoboken,  N.  J  

Salt  Lake  City   Utah             .     . 

Pampaluna   Spain    

«                 it 

Port  Simpson,  B.  C  
Burroughs  Bay,  Alaska     .... 
Wrangell,                 "           .... 
Sitka,                        "           .... 
St.  Paul's  Island,    "           .... 
Juneau,                     "           .... 
Pyramid  Harbor,    "           .... 
Yakutat  Bay,                      .... 

i  Smith  :  "  United  States  Coast  and  Geodetic  Survey  Report  for  1884,"  App.  14- 
2  Preston  :  "  United  States  Coast  and  Geodetic  Survey  Report  for  1860,    App.  12. 
3  Preston  :  Ibid.  1888,  App.  14. 
4  Mendcnhall  :   Ibid.  1891,  App.  15. 
5  Defforges  :  "  Comptes  Rendus,"  vol.  118,  p.  231. 

76  %Z&  ;nUd  LC  A^  *£&?&&&  Seances  de  ,a  Co-nu-lon  Penna- 

nente  de  1'Association  Geodesique  International,     1893. 
8  Pierce:  "  U.  S.  C.  and  G.  S.  Report  1876,  App.  15,  and  1881,  App.  17. 
9  Messerschmidt  :  Same  reference  as  7. 

*  In  all  the  values  given  under  references  1-4  gravity  at  Washington  has  been  taken  at  980. ,00,  and  the  others 
derived  from  that  by  comparative  experiments  with  invariable  pen. 
SMITHSONIAN  TABLES. 

103 


TABLE  1 1 4. 


SUMMARY  OF  RESULTS  OF  THE  VALUE  OF  GRAVITY  (f/)  AT  STATIONS 
IN  THE  UNITED  STATES,  OCCUPIED  BY  THE  U.  S.  COAST  AND 
GEODETIC  SURVEY  DURING  THE  YEAR  1894.* 


Station. 

Latitude. 

Longitude. 

Elevation. 

g 

observed. 

Atlantic  Coast. 

0        f         II 

O        1          II 

Metres. 

Dynes. 

42   21    ^1 

71    O1    SO 

22 

980.382 

Cambridge,  Mass  

*r        '       JO 
42    22   48 

/           3    0 

7i  07  45 

14 

980.384 

Princeton,  N.  J.          .... 

40  20  57 

74  39  28 

64 

980.164 

Philadelphia,  Pa  

39  57  06 

75  JI  40 

16 

980.182 

Washington,  C.  &  G.  S.     . 

38  53  J3 

77  oo  32 

14 

980.098 

Washington,  Smithsonian.         .        .    ; 

38  53  20 

77  oi  32 

10 

980.  loot 

Appalachian  Elevation. 

Ithaca,  N.  Y  ;  .    ; 

42  27  04 

76  29  oo 

247 

980.286 

Charlottesville,  Va  

38  02  01 

78  30  16 

1  66 

979.924 

Deer  Park,  Md.          .        . 

39  25  02 

79  19  50 

770 

979.921 

Central  Plains. 

Cleveland,  Ohio          .... 

41    30   22 

81  36  38 

2IO 

980.227 

Cincinnati,  Ohio          .... 

39  08  20 

84    25    20 

245 

979.990 

Terre  Haute,  Ind  

39  28  42 

87  23  49 

I51 

980.058 

Chicago   111  

41    47    2S 

87  T.6  01 

182 

980.264 

St.  Louis,  Mo  

*r      TV        j 
38    38    03 

/    3         3 
90    12    13 

*54 

979.987 

Kansas  City,  Mo  

39  °5  5° 

94  35  21 

278 

979.976 

Ellsworth,  Kan.  .        .        .        .        »  1 

38  43  43 

98  13  32 

469 

979.912 

Wallace,  Kan  '  ,  . 

38  54  44 

101  35  26 

1005 

979.741 

Colorado  Springs,  Col.       .                 • 

38  5°  44 

104  49  02 

1841 

979.476 

Denver,  Col  -    •  I- 

39  40  36 

104  56  55 

1638 

979-595 

Rocky  Mountains. 

Pike's  Peak,  Col.        .        .        .      .  .  r 

38  50  20 

105  02  02 

4293 

978.940 

Gunnison,  Col.    .         .         .         .      "  .  , 

38  32  33 

106  56  02 

2340 

979.328 

Grand  Junction,  Col. 

39  04  09 

108  33  56 

1398 

979.619 

Green  River,  Utah     .         .         .    •    .  , 
Grand  Canyon,  Wyo.          .         .         .  ! 

38  59  23 
44  43  16 

no  09  56 
no  29  44 

1243 
2386 

979.622 
979-885 

Norris  Geyser  Basin,  Wyo.        .        .  ; 

44  44  09 

no  42  02 

2276 

979.936 

Lower  Geyser  Basin,  Wyo. 

44  33  2I 

I  10  48   08 

2  2OO 

979.918 

Pleasant  Valley,  Jet.,  Utah 
Salt  Lake  City,  Utah         .        .        . 

39  5°  47 
40  46  04 

III    OO   46 

in  53  46 

2191 

I322 

979.498 
979.789 

TABLE  115. 

LENGTH  OF  SECONDS  PENDULUM  AT  SEA  LEVEL  FOR  DIFFERENT 

LATITUDES.* 


1 

fj 

f| 

1 

51 

It 

3 

if 

1—  1  O 

S 

fl 

I 

3 

H 

1 

tuO 

0 

99.0910 

1.996034 

39.0121 

1.591200 

50 

99.4014 

1  -997  393 

39-  J  344 

I-592558 

5 

.0950 

6052 

•oi37 

1217 

ss 

•4459 

7587 

.1520 

2753 

IO 

.1079 

6104 

.0184 

1270 

60 

.4876 

7770 

.1683 

2935 

'S 

.1265 

6190 

.0261 

1356 

6S 

•5255 

7935 

.1832 

3100 

20 

.1529 

6306 

•0365 

1471 

70 

.5581 

8077 

.1960 

3242 

25 

99-1855 

1.996448 

39-0493 

1.591614 

75 

99-5845 

1.998192 

39-2065 

J-593358 

3° 

.2234 

6614 

.0642 

1779 

80 

.6040 

8277 

.2141 

•3442 

35 

.2651 

6796 

.0806 

1962 

85 

.6160 

8329 

.2188 

•3494 

40 

.3096 

6991 

.0982 

2157 

90 

.6200 

8347 

.2204 

•3512 

45 

•3555 

7192 

.1163 

2357 

*  G.  R.  Putnam,  Phil.  Soc.  of  Washington,  Bull.  vol.  xiii. 

t  Taken  as  standard.     The  other  values  were  obtained  from  this  by  means  of  invariable  pendulums. 
J  Calculated  from  force  of  gravity  table  by  the  formula  l=g]  IT-.     For  each  100  feet  of  elevation  subtract  0.000596 
centimetres,  or  0.000235  inches,  or  .0000196  feet. 

SMITHSONIAN  TABLES. 

104 


TABLE  116. 


LENGTH  OF  THE  SECONDS  PENDULUM.* 


Date  of 
determi- 
nation. 

llll 

3  °  «  rt 

fc-s** 

Range  of  latitude  included  by 
the  stations. 

Length  of  pendulum  in  metres 
for  latitude  </>. 

Correspond- 
ing length 
of  pendulum 
forlat.45°. 

Refer- 
ence. 

1799 

15 

From  +  67°  05'  to  —  33°  56' 

0.990631  -f-  .005637  sin2^ 

0-99345° 

I 

1816 
1821 

38 

"     +74°  53'    '  —  51°  21' 
"      -f  38°  40'    '  —  60°  45' 

0.990743  4-  -005466  sin24> 
0.990880  -f  -005340  sin2  (j> 

0.993976 
0-993550 

2 

3 

1825 

25 

"     +79°  So'    '  —i  2°  59' 

0.990977  -j-  -005142  sin20 

0.993548 

4 

1827 

41 

+  79°  So;    '  -5'°  35' 

0.991026-]-  .005072  sin2^> 

0.993562 

5 

1829 

5 

o°    o'    '  +67°  04' 

0-990555  T  -005679  sin2^ 

0-993395 

6 

1830 

49 

"     +  79°  5i'   "  -  5i°  35' 

0.991017  -f-  -005087  sin2^> 

0.993560 

7 

1833 

— 

0.990941  -f-  .005142  sin20 

0.993512 

8 

1869 
1876 

5i 

73 

"     +79°5o/  "  -51°  35' 
"     +79°  5°'  "  —62°  56' 

0.990970  -f  .005185  sin20 
0.991011  -j-  .005105  sin'20 

o-993554t 
o-993563 

9 

10 

1884 

123 

"     +79°  50'  "  -62°  56' 

0.990918  -}-  -005262  sin2^ 

0-993549 

ii 

Combining  th< 

^  above  results  .... 

0.990910  +  -005290  sin2? 

0-993555 

12 

'  In  1884,  from  the  series  of  observations  used  by  Dr.  Fischer,  Dr.  G.  W.  Hill  13  found 
/=     0.9927148  metre 

+  0.0050890  p~4  (sin2  <j>  —  }) 

-j-  O.OOOO979  p~4  COS2  0  COS  (20)'  +29°  04") 


00001355  p~5  (sin3^  — 
+  0.0005421  p~5(sin20  — 


sn 
cos  (j)  cos  (&>' 


217°  51') 


--  0.0002640  p~5  sin  0  cos2  fy  cos  (2w  -\-  4°  49') 

-j-  o.oooi  248  p~5  cos3  <t>  cos  (3«'  -j-  1  10°  24') 

-j-  0.0001489  p-6  (sin4  (f>  —  |  sin2  0  +  ^) 

-j-  0.0007386  p~6  (sin3  <j>  —  f  sin  0)  cos  <j>  cos  («'  -f-  3°  02') 

-j-  0.0002175  p~°  (sin2  (j>  —  |)  cos2  0  cos  (zw  -\-  262°  17') 

-j-  0.0003126  p~6  sin  (j>  cos3  ^  cos  (30?'  +  T48°  20') 

-j-  0.0000584  p-6  cos4  (j)  cos  (4«'  +  248°  19') 

where  (j>  is  the  geocentric  latitude,  a'  the  geographical  longitude,  and  p  a  factor,  varying 
with  the  latitude,  such  that  the  radius  of  the  earth  at  latitude  <f>  is  ap  where  a  is  the  equa- 
torial radius  of  the  earth. 


1  Laplace  :  "Traite  de  Mecanique  Celeste,"  T.  2,  livre  3,  chap.  5,  sect.  42. 

2  Mathieu :  "  Sur  les  experiences  du  pendule ;"  in  "  Connaissance  des  Temps  1816," 
Additions,  pp.  314-341,  p.  332. 

3  Biot  et  Arago  :  "  Recueil  d'Observations  geodesiques,  etc."     Paris,  1821,  p.  575. 

4  Sabine  :  "  An  Account  of  Experiments  to  determine  the  Figure  of  the  Earth,  etc.,  by 
Sir  Edward  Sabine."     London,  1825,  p.  352. 

5  Saigey  :  "  Comparaison  des  Observations  du  pendule  a  diverses  latitudes  ;  faites  par 
MM.  Biot,  Kater,  Sabine,  de  Freycinet,  et  Duperry ;  "  in  "  Bulletin  des  Sciences  Mathe- 
matiques,  etc.,"  T.  i,  pp.  31-43,  and  171-184.     Paris,  1827. 


pp.  32-33 ;  and  Puissant :  "  Traite  de  geodesic,"  T.  2,  p.  464. 

9  Unferdinger:  "Das  Pendel  als  geodatisches  Instrument;"  in  Grunert's  "Archiv," 

10'  Fischer :  "  Die  Gestalt  der  Erde  und  die  Pendelmessungen ;  "  in  "  Ast.  Nach."  1876, 

11  Helmert:  "Die  mathematischen  und  physikalischen  Theorieen  der  hoheren  Geo- 
dasie,  von  Dr.  F.  R.  Helmert,"  II.  Theil.     Leipzig,  1884,  p.  241. 

12  Harkness. 

13  Hill,  Astronomical  paper  prepared  for  the  use  of  the  "American  Ephemeris  and 
Nautical  Almanac,"  vol.  3,  p.  339. 


*  The  data  here  given  with  regard  to  the  different  determinations  which  have  been  made  of  the  length  of  the 
seconds  pendulum  are  quoted  from  Harkness  (Solar  Parallax  and  its  Related  Constants,  Washington,  1891). 

t  Calculated  from  a  logarithmic  expression  given  by  Unferdinger. 
SMITHSONIAN  TABLES. 


105 


TABLE  117. 

MISCELLANEOUS  DATA  WITH  REGARD  TO  THE   EARTH  AND  PLANETS, 


Length  of  the  seconds  pendulum  at  sea 

level =  /  =  39.012540  -f-  0.208268  sin2  <j>  inches. 

=  3.251045  -j-  0.017356  sin'2  ty  feet. 
=  0.9909910  -f  0.005290  sin*  (j>  metres. 
Acceleration  produced  by  gravity  per  sec- 
ond per  second  mean  solar  time     .         .     =^=32.086528  -f-  0.171293  sin2  <p  feet. 

=  977.9886  -|-  5.2210  sin2  ^  centimetres. 

Equatorial  semidiameter    ....    =a  =  20925293  -{-  409.4  feet. 

=  3963.124  -j-  0.078  miles. 
=  6377972-]-  124.8  metres. 

Polar  semidiameter =6  —  20855590-}-  325.1  feet. 

=  3949.922  -J-  0.062  miles. 
=  6356727  -J-  99.09  metres. 

One  earth  quadrant =393775819^  4927  inches. 

=  32814652  -j-  410.6  feet. 
=  6214.896-1-0.078  miles. 
=  10001816  ^  125.1  metres. 

Flattening    =f!—*L== T      * 

a          300.205  J-  2.964 

Eccentricity  =  a  ~~     =  0.006651018. 
a* 

Difference  between  geographical  and  geocentric  latitude  =  0  —  $' 

=  688.2242"  sin  2  <t>  —  1.1482"  sin  4  0  -f~°>OO26"  sin  6  <}>. 

Mean  density  of  the  Earth  =  5.576  ^  0.016. 
Surface  density  of  the  Earth  =  2.56  J^  0.16. 

Moments  of  inertia  of  the  Earth ;  the  principal  moments  being  taken  as  A,  J3,  and  C, 
and  C  the  greater : 

C—  A  f  i 

-u—  0.0032652,  =  555^; 

C  —  A  =  0.001064767  Ed2  \ 
A  =  B  =  0.325029  Ea* ; 
C—  0.326094  Ea?; 
where  E  is  the  mass  of  the  Earth  and  a  its  equatorial  semidiameter. 

Length  of  sidereal  year  =  365.2563578  mean  solar  days  ; 

=  365  days  6  hours  9  minutes  9.314  seconds. 

Length  of  tropical  year 

=  365.242199870  —  0.0000062124  —    ?—5-  mean  solar  days  ; 

=  365  days  5  hours  48  minutes  (  46.069  —  0.53675  —        ^°  j  seconds. 
Length  of  sidereal  month 


=  27.321661162  —  0.00000026240  —         —  days ; 


=  27  days  7  hours  43  minutes  (11.524  —  0.022671  — —  J  seconds. 

Length  of  synodical  month 


29.530588435  —  0.00000030696 -      days  ; 


=  29  days  12  hours  44  minutes  (  2.841  — 0.026522  —         -  j  seconds. 
Length  of  sidereal  day  =  86164.09965  mean  solar  seconds. 

N.  B.  —  The  factor  containing  /  in  the  above  equations  (the  epoch  at  which  the  values  of 
the  quantities  are  required)  may  in  all  ordinary  cases  be  neglected. 


*  Harkness,  "  Solar  Parallax  and  Allied  Constants.' 
SMITHSONIAN  TABLES. 

1 06 


TABLE  117, 
MISCELLANEOUS  DATA  WITH    REGARD  TO  THE  EARTH  AND  PLANETS. 


MASSES  OF  THE  PLANETS. 

Reciprocals  of  the  masses  of  the  planets  relative  to  the  Sun  and  of  the  mass  of  the  Moon 
relative  to  the  Earth  : 

Mercury  =  8374672  -{-  1765762. 
Venus  '   =  408968  -j-  1874. 
Earth*    =327214-1-624. 
Mars        =  3093500  -J-  3295. 
Jupiter    =  1047.55  i  o-2°- 
Saturn     =  3  50 1 .6  ^  0.78. 
Uranus    =  22600  -j-  36. 
Neptune  =  18780  -^  300. 

Moon      =81.068^0.238. 


Mean  distance  from  Earth  to  Sun  =  92796950  -J-  59715  miles  ; 

=  149340870-1-96101  kilometres. 

Eccentricity  of  Earth's  orbit  =  e\ 

=  0.016771049  —  0.0000004245  (t —  1850)  —0.000000001367  ( — - J  . 

Solar  parallax  =  8.80905"  ^  0.00567". 
Lunar  parallax  =  3422.542 16"  ^  o.  12533". 

Mean  distance  from  Earth  to  Moon  =  60.26931 5  -J-  0.002502  terrestrial  radii  j 

=  238854.75  j-  9.916  miles ; 
=  384396-01  ^  15-958  kilometres. 

Lunar  inequality  of  the  Earth  =  L  =  6.52294"  -|-  0.01854". 

Parallactic  inequality  of  the  Moon  =  Q=  124.95126" ^ 0.08197". 

Mean  motion  of  Moon's  node  in  365.25  days  =  /t=  — 19°  21'  19.6191" +  0.14136"  — ^~- 

Eccentricity  and  inclination  of  the  Moon's  orbit  =  ^2  =  0.054899720. 

Delaunay's  7  =  sin  1 7=  0.044886793. 
7  =  5°  08'  43-3546". 

Constant  of  nutation  =  9.22054"  -J-  0.00859"  +  o.oooooo/H77  (t—  1850). 
Constant  of  aberration  =  20.45451"  ^  0.01258". 

Time  taken  by  light  to  traverse  the  mean  radius  of  the  Earth's  orbit 

=  498.00595  -J-  0.30834  seconds. 

Velocity  of  light  =  186337.00  -J-  49.722  miles  per  second. 

=  299877.64  ^  80.019  kilometres  per  second. 


*  Earth  +  Moon. 
SMITHSONIAN  TABLES. 

107 


TABLE  118. 


AERODYNAMICS. 

The  pressure  on  a  plane  surface  normal  to  the  wind  is  for  ordinary  wind  velocities  expressed  by 


•where  k  is  a  constant  depending  on  the  units  employed,  w  the  mass  of  unit  volume  of  the  air, 
a  the  area  of  the  surface  and  v  the  velocity  of  the  wind.*  Engineers  generally  use  the  table  of 
values  of  /"given  by  Smeaton  in  1759.  This  table  was  calculated  from  the  formula 

P=.  00492  z/2 

and  gives  the  pressure  in  pounds  per  square  foot  when  v  is  expressed  in  miles  per  hour.  The 
corresponding  formula  when  v  is  expressed  in  feet  per  second  is 

P=.  00228  z/2 

Later  determinations  do  not  agree  well  together,  but  give  on  the  average  somewhat  lower 
values  for  the  coefficient.  The  value  of  w  depends,  of  course,  on  the  temperature  and  the  baro- 
metric pressure.  Langley'st  experiments  give  kiv  —  .  00166  at  ordinary  barometric  pressure  and 
10°  C.  temperature. 

For  planes  inclined  at  an  angle  a  less  than  90°  to  the  direction  of  the  wind  the  pressure  may 
be  expressed  as  /*a  =  FaP$Q. 

Table  118,  founded  on  the  experiments  of  Langley,  gives  the  value  of  Fa  for  different  values  of 
«.  The  word  aspect,  in  the  headings,  is  used  by  him  to  define  the  position  of  the  plane  relative  to 
the  direction  of  motion.  The  numerical  value  of  the  aspect  is  the  ratio  of  the  linear  dimension 
transverse  to  the  direction  of  motion  to  the  linear  dimension,  a  vertical  plane  through  which  is 
parallel  to  the  direction  of  motion. 


TABLE  118.— Values  of  Fa  In  Equation  Pa-PaP9o. 


Plane  30  in.  X  4.8  in. 

Aspect  6  (nearly). 

Plane  12  in.  X  12  in. 
Aspect  i. 

Plane  6  in.  X  24  in. 
Aspect  i. 

a 

^« 

a 

*; 

a 

K 

0° 

0.00 

0° 

o.oo 

0° 

o.oo 

5 

0.28 

5 

0.15 

5 

0.07 

10 

0.44 

10 

0.30 

10 

0.17 

15 

20 

0.55 

0.62 

15 

20 

0.44 
0.57 

'5 

20 

0.29 

0.43 

25 

0.66 

25 

0.69 

25 

0.58 

30 

0.69 

30 

0.78 

30 

0.71 

35 

0.72 

35 

0.84 

— 

40 

0.74 

40 

0.88 

— 

— 

45 

0.76 

45 

0.91 

- 

- 

50 

0.78 

50 

- 

- 

- 

*  The  pressure  on  a  spherical  surface  is  approximately  0.36  that  on  a  plane  circular  surface  of  the  same  diameter 
as  the  sphere  ;  on  a  cylindrical  surface  with  axis  normal  to  the  wind,  about  0.5  that  on  a  rectangular  surface  of  length 
equal  to  the  length,  and  breadth  equal  to  the  diameter  of  the  cylinder. 

t  The  data  here  given  on  Professor  Langley's  authority  were  communicated  by  him  to  the  author. 

SMITHSONIAN  TABLES. 

108 


TABLE    119, 


AERODYNAMICS. 


On  the  basis  of  the  results  given  in  Table  118  Langley  states  the  following  condition  for  the 
soaring  of  an  aeroplane  76.2  centimetres  long  and  12.2  centimetres  broad,  weighing  500  grammes, 
—  that  is,  a  plane  one  square  foot  in  area,  weighing  i.i  pounds.  It  is  supposed  to  soar  in  a 
.horizontal  direction,  with  aspect  6. 


TABLE  119.  -  Data  for  the  Soaring  of  Planes  76.2  X  12.2  cms.  weighing  500  Grammes,  Aspect  6. 


Inclination 

Soaring  speed  v. 

Work  expended  per  minute 
(activity). 

Weight  of  planes  of  like 
form,  capable  of  soaring 
at  speed  v  with  the  ex- 
penditure of  one  horse 

to  the  hori- 

power. 

zontal  0. 

Metres  per 
sec. 

Feet  per 
sec. 

Kilogramme 
metres. 

Foot 
pounds. 

Kilogrammes. 

Pounds. 

2° 

2O.O 

66 

24 

174 

95.0 

209 

5 

I5.2 

50 

41 

297 

55-5 

122 

10 
15 

3° 

12.4 
11.2 

10.6 

41 

37 
35 

i 

"75 

474 
I2685 

34-8 
26.5 
13.0 

3 

29 

45 

II.  2 

37 

336 

2434 

6.8 

'5 

weight 
In  general,  if  P=-~ 


Soaring  speed  v  — 
Activity  per  unit  of  weight  =  v  tan  a 

The  following  data  for  curved  surfaces  are  due  to  Wellner  (Zeits.  fur  Luftschifffahrt,  x.,  Oct. 
1893). 

Let  the  surface  be  so  curved  that  its  intersection  with  a  vertical  plane  parallel  to  the  line  of 
motion  is  a  parabola  whose  height  is  about  ^  the  subtending  chord,  and  let  the  surface  be 
bounded  by  an  elliptic  outline  symmetrical  with  the  line  of  motion.  Also,  let  the  angle  of  incli- 
nation of  the  chord  of  the  surface  be  a,  and  the  angle  between  the  direction  of  resultant  air 
pressure  and  the  normal  to  the  direction  of  motion  be  0.  Then  /3  <  o,  and  the  soaring  speed  is 


-Vi 


.,  while  the  activity  per  unit  of  weight  =z/tan  ft. 


k  Fa.  cos  /8 
The  following  series  of  values  were  obtained  from  experiments  on  moving  trains  and  in  the 

wind. 

Angle  of  inclination  a  =  -  3°  °°  +  3°  6°              9°           1  2° 

Inclination  factor  Fa  =  0.20  0.50  0.75  0.90 

tan  0=  o.o  i  0.02  0.03  0.04  o.io          0.17 

Thus  a  curved  surface  shows  finite  soaring  speeds  when  the  angle  of  inclination  a  is  zero  or  even 
.slightly  negative.  Above  a  =  12°  curved  surfaces  rapidly  lose  any  advantage  they  may  have  for 
•small  inclinations. 


SMITHSONIAN  TABLES. 


109 


TABLES  120,  121. 


TERRESTRIAL    MAGNETISM. 


TABLE  120.  -  Total  Intensity  of  the  Terrestrial  Magnetic  Field. 

This  table  gives  in  the  top  line  the  total  intensity  of  the  terrestrial  magnetic  field  for  the  longitudes  given  in  the  first 
column  and  the  latitudes  given  in  the  body  of  the  table.  Under  the  headings  13,  13.5,  and  13.75  there  are  some- 
times several  entries  for  one  longitude.  This  indicates  that  these  lines  of  total  force  cut  the  same  longitude  line 
more  than  once.  The  isodynamic  lines  are  peculiarly  curved  and  looped  north  of  Lake  Ontario.  The  values  are 
for  the  epoch  January  i,  1885,  and  the  intensities  are  in  British  and  C.  G.  S.  units. 


Longi- 
tude. 

10.5 

or 
.4841 

II.  O 

or 
.5072 

"•5 
or 

530  1 

12.0 

or 
•5533 

12.5 

or 
•5764 

13.0  or  .5994 

13.5  or  .6225 

13.75  or  .6340 

0 

67 

68 

70 
72 
75 

76 

1 

81 

82 

83 

& 

87 

90 

92 
95 

100 

105 

110 

"5 
1  20 
124 

0 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

44-5 

45-5 

,0  ,, 

43-  l 

45.2 

- 

- 

- 

- 

- 

40.6 

~>f>  -7 

- 

- 

- 

- 

- 

- 

- 

jO-7 

- 

447 
43-6 
43-3 
43-9 
41.4 

41.2 
41.0 
40.8 
41.1 
41.9 

41.6 
41.7 
41.2 
41.4 
43-6 

45-2 

454 
45-2 
44.6 
41.9 

42.1 

44-3 
43-6 

45-8 
45.8 

i 

- 

19.6 
19.8 
2O.O 

20.1 
2O.  I 
2O.O 
2O.O 

21-7 

23.2 

22.6 
22.8 
22.8 

22.8 

22.7 
22.2' 
22.3 
22.5 

22.5 

22-3 
22-3 
22.8 
24.4 

26.9 
29.T 
30-7 

24-5 
24-5 
24-5 

24.6 
24.8 
25.0 

31.2 
31.8 

34-7 

27.9 
27.1 

26.4 
26.6 
27.9 
28.3 
28.6 

29.9 

29-3 
28.3 
30.0 

33-1 

344 
36.2 

37-8 
39-6 

31.2 
31.2 

3r-3 
31.2 
30.8 
30.6 
304 

3r-9 
33-3 
33-i 
34-1 
36.1 

37-7 
40.1 

42.3 

3°4 
36.0 

34-i 
35-1 

35-5 

35-5 
35-2 
344 
35-3 

35-5 

36.6 
$7-4 

37-2 
39-o 
39-8 

41.6 

44-5 
46.4 

40.2 
47-6 
48.0 
'484 

49.1 
50.2 

- 

- 

45-5 
45-2 
43-2 

43-2 
44-7 
43-7 

46.1 

474 

47-7 

48.2 
48.2 

- 

- 

- 

42.7 
44.8 

47.0 

- 

44.2 

TABLE  121.— Secular  Variation  of  the  Total  Intensity. 

Values  in  British  units  of  total  intensity  of  terrestrial  magnetic  force  at  stations  given  in  the  first  column  and  epochs 
January  i  of  the  years  given  in  the  top  line. 


Station. 

1840 

1845 

1850 

1855 

1860 

1865 

1870 

1875 

1880 

1885 

Cambridge  .  . 

13.48 

'3-33 

13.21 

13.22 

13-37 

1345 

13.49 

13-39 

13.14 

12.79 

New  Haven  . 

1347 

13.40 

13-2S 

13.  1  1 

13.20 

13-33 

I341 

1341 

13.29 

I3-05 

New  York 

13  56 

'351 

13-39 

'3-27 

13.32 

13.36 

12.99 

Sandy  Hook  . 
Albany      .     . 

13-70 
13.68 

J3-59 
13-65 

I3-72 

13-80 

I3-23 
I3-87 

13.35 
13.93 

13.40 
13.92 

13-39 
13.82 

I3-30 
13.61 

I3-I3 
I3-27 

Philadelphia  . 
Baltimore  . 
Washington  . 

'3-56 
r343 

13-44 

*345 
13-36 

T345 
13-38 

r347 
13-37 
13-34 

13-44 
!3-39 

13-55 
13.46 
13.42 

13-58 
13.48 
13.42 

13-57 
13.48 

I3-38 

13-49 
I3-38 
13.29 

I3-25 
13.22 
13.20 

Toronto     .     . 
Cleveland 

14.03 
13-85 

13-93 
I3-78 

13-95 
'3-76 

12.75 

13.82 
13-78 

13.82 
I3-83 

13-77 
13.84 

I3-78 
13.81 

I3-78 
13-74 

13.76 
13.61 

Detroit  .     .     . 

I3-85 

13.80 

.3.7. 

13.68 

13-72 

1375 

I3-76 

I3-78 

13-73 

13.62 

*  Tables  120-125  have  been  compiled  from  a  very  full  discussion  of  the  magnetic  dip  and  intensity  for  the  United 
States  and  adjacent  countries,  given  in  Appendix  6  of  the  Report  of  the  United  States  Coast  and  Geodetic  Survey 
for  1885.  Later  Reports  of  the  survey  have  been  consulted,  particularly  in  connection  with  the  extrapolation  of  the 
values  of  horizontal  intensity  to  1890  and  1895,  but  most  of  the  data  are  taken  from  Mr.  Schott's  Appendix  to  the  1885 
Report. 

SMITHSONIAN  TABLES. 

110 


TERRESTRIAL    MAGNETISM. 

TABLE  122.  — Values  of  the  Magnetic  Dip. 


TABLES  122,  123. 


This  table  gives  for  the  epoch  January  i,  1885,  the  values  of  the  magnetic  dip,  stated  in  first  column,  corresponding 
to  the  longitudes  given  in  the  top  line  and  the  latitudes  given  in  the  body  of  the  table.  Thus,  for  longitude  95° 
and  latitude  30°  the  dip  was  59°  on  January  i,  1885.  The  longitudes  are  west  of  Greenwich.  For  positions  above 
the  division  line  in  the  table  the  dip  was  increasing,  and  for  positions  below  that  line  decreasing,  in  1885. 


Dip. 

Longitudes  west  of  Greenwich. 

66° 

7o° 

75° 

80° 

85° 

90° 

95° 

100° 

105° 

110° 

us0 

120° 

124° 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

O 

o 

44 

- 

- 

- 

- 

- 

17.9 

I8.4 

19.1 

19.6 

- 

- 

- 

- 

45 

- 

- 

- 

- 

- 

18.7 

19.2 

19.8 

20.3 

- 

- 

- 

-( 

6 

— 

— 

— 

— 

— 

19.2 

19.8 

20.6 

21.  1 

- 

— 

— 

-, 

7 

- 

- 

- 

- 

- 

2O.O 

20.5 

21.2 

21.8 

- 

- 

- 

- 

8 

— 

— 

I7.9 

- 

— 

20-5 

21.2 

21.9 

22.5 

23-3 

— 

— 

- 

9 

- 

- 

I8.7 

- 

- 

21.2 

21.9 

22.6 

23.2 

24.0 

- 

~ 

- 

50 

- 

- 

- 

- 

21.4 

22.1 

__  0 

22.7 

23-5 

24.1 

->  A    ft 

24.7 

- 

- 

- 

i 

22.O 

23.6 

24.3 

24.O 

25-5 

~ 

~ 

"" 

2 

— 

— 

— 

22.4 

23.0 

23-7 

24.4 

25.1 

2|.6 

26.3 

27.4 

— 

— 

3 
4 

«- 

- 

- 

23-3 

24.0 

23.9 
24.7 

24.5 
25-3 

25.2 
26.O 

26.7 

26.5 
27.2 

27.1 

28.1 

28.2 

29.0 

- 

- 

55 

_ 

— 

_ 

24.8 

25-5 

26.1 

26.8 

27-5 

28.1 

28.9 

29.9 

— 

_ 

6 

- 

- 

24.7 

25.6 

26.3 

26.9 

27.5 

28.1 

28.9 

29-7 

30.6 

- 

- 

7 

- 

- 

- 

26.4 

27.1 

27.7 

28.3 

28.9 

29.7 

30.6 

3J4 

- 

- 

8 

— 

— 

— 

27-3 

27.9 

28.5 

29.1 

29.8 

3°-5 

314 

32.3 

— 

- 

9 

- 

- 

- 

28.0 

28.7 

29.4 

3O.O 

3O.6 

324 

33-3 

344 

- 

60 

- 

- 

- 

28.6 

29.6 

30-2 

30-8 

31-5 

324 

33-4 

34-3 

35-3 

- 

i 

- 

- 

- 

29-9 

30.3 

30-9 

|  31-7 

32-4 

33-3 

34-2 

35-3 

•36.2 

- 

2 

3 

- 

: 

— 

30.6 

31.6 

32.0 

31-9 

32.7 

32.5 
33-6 

33-3 
34-2 

34-3 

III 

36-3 
37-1 

£ 

39-o 

4 

- 

- 

- 

32.7 

33-2 

33-6 

34-5 

35-2 

36.1 

37-2 

38.1 

39-o 

40-3 

65 

_ 

_ 

_ 

33-5 

34-o 

34-6 

35-5 

36.2 

37-i 

38.2 

39-2 

40-3 

41.5 

6 

— 

— 

— 

34-3 

35-o 

35-8 

36-5 

37-2 

38-1 

39-2 

40.3 

4!-5 

42-5 

7 

_ 

_ 

35.1 

35-3 

35-9 

36.6 

38.2 

39-  i 

40.2 

41.4 

42-5 

43-6 

8 

_ 

_ 

35-8 

36.0 

36.6 

37-5 

38.2 

39-2 

40.0 

41.2 

42.4 

43-6 

44-7 

9 

- 

- 

37  -o 

37-5 

37-6 

38.5 

39-2 

40.0 

41.2 

42.2 

43-5 

44-6 

45-7 

70 

_ 

_ 

38.0 

38-5 

39-o 

39-6 

40.4 

41.0 

42.1 

43-3 

44-5 

45-6 

46.9 

i 

_ 

_ 

39-  i 

39-5 

39-8 

40-7 

41.1 

41.8 

43-2 

44-3 

45-7 

47-2 

47-9 

2 

_ 

_ 

40.4 

40-3 

40.9 

41.6 

42.1 

43-  r 

44-3 

45-5 

47.1 

48.6 

49-2 

3 

_ 

41.7 

41.2 

41.9 

42.2 

42.7 

43-4 

44-4 

45-5 

46.9 

48.6 

50.0 

— 

4 

43-5 

43-i 

42.9 

43-  i 

43-4 

43-9 

44-5 

45-6 

46.7 

48-3 

49-7 

— 

— 

75 

44-9 

44-5 

44-3 

44.0 

44-5 

45-° 

45-7 

46-7 

48.0 

49-5 

51.0 

- 

- 

6 

45-7 
47-3 

45-9 
47.6 

45-5 
46.7 

45-4 
46.9 

45-5 
47-o 

46.1 

47-4 

47.1 
48.3 

48.2 
49-4 

49-5 
50.6 

50-7 

- 

- 

- 

8 

— 

48.2 

48.0 

48.8 

49-7 

50-7 

51.8 

- 

— 

"~ 

— 

9 

- 

- 

- 

49-3 

49-3 

- 

51.0 

5r-9 

— 

~ 

~~ 

~ 

" 

80 

- 

- 

— 

5°4 

504 

~ 

•• 

" 

" 

TABLE  123.  —  Secular  Variation  of  the  Magnetic  Dip. 

Values  of  magnetic  dip  at  stations  given  in  the  first  column,  and  epochs,  January  i,  of  the  years  given  in  the  top  line. 


Station. 

1840 

1845 

1850 

1855 

1860 

1865 

1870 

1875 

1880 

1885 

Cambridge  . 
New   Haven 
New  York   . 
Sandy  Hook 
Albany    .     . 

74-25 
7347 
72.75 
72.63 

74-75 

74-29 
73-51 
72.73 
72.61 
74.80 

74-35 
73-56 
72-75 
72.63 
74.88 

74.40 
73.61 
72.78 
72.66 
74.96 

74.42 

73-64 
72.80 
72.68 
75-02 

74.38 
73.62 
72.78 
72.66 
75.02 

74.26 

73-54 
72.71 

72.59 
74.95 

74.02 
73-38 
72-56 
72-44 
74-77 

73-65 
73-" 
72-31 
72.19 
74.46 

73-J2 
72-72 
71-93 
71.81 

73-99 

Philadelphia 
Baltimore     . 
Washington 
Toronto  . 
Cleveland     . 

71.99 
7J-74 
71-39 

75.28 

73-22 

72.02 
71.66 
7i-39 
75-25 
73-I9 

72.08 
71.66 
71-38 
75-32 
73.21 

72-15 
71.69 

7i-36 
75-39 
73-24 

72.20 
7I-74 
7I-32 
754^ 
73.28 

72.21 
71-77 
7I-25 
75-35 
73-29 

72.16 
71.76 
7I-I5 

75-27 
73-27 

72.02 
71.67 
71.00 
75-20 
73-iS 

71-77 
71.48 
70.80 
75-°3 
73-°3 

7».38 
71.16 

70-55 
74.§§ 
72.78 

Detroit    .     . 

73.61 

73-61 

73-63 

73-66 

73-68 

73.69 

73-67 

73.60 

7347 

73.28 

SMITHSONIAN  TABLES. 


Ill 


TABLES  124,  125. 


TERRESTRIAL  MAGNETISM. 

TABLE  124.  -  Horizontal  Intensity. 


This  table  gives,  for  the  epoch  January  i,  1885,  the  horizontal  intensity,  ff,  corresponding  to  the  longitudes  in  the  top 
line  and  the  latitudes  in  the  body  of  the  "table.  At  epoch  1885  the  force  was  increasing  for  positions  above  the 
division  line,  and  was  decreasing  for  positions  below  the  division  Hue. 


H 

\  in  British 
[     units. 

Longitudes  west  of  Greenwich. 

H 
inCG.S. 

units. 

v 

70° 

75° 

80° 

85* 

90° 

95° 

100° 

105° 

110° 

115° 

<*>* 

114° 

2.50 

o 

0 

0 

0 

49-8 

0 

0 

o 

o 

0 

o 

o 

0 

.1153 

2.75 

_ 

« 

_ 

48-5 

4^.8 

49-8 

_ 

- 

- 

- 

- 

_ 

- 

.1868 

3.00 
325 
3-50 

48-3 

45-5 
43-2 

47-3 
45-6 
43-8 

46.6 

45-5 
43-6 

47.2 

45-8 
44.0 

47-6 
46.1 
44-6 

48.5 
46.7 

49-1 
47.6 
45-8 

50.1 

48.5 

47-2 

_ 

_ 

_ 

- 

- 

.1383 
.1498 
.1614 

3.75 

- 

42.2 

42.5 

42.6 

43-2 

43-6 

44-6 

45.8 

47-3 

48.4 

49.4^ 

- 

- 

.1729 

4.00 

- 

40.7 

41.2 

41-5 

42.1 

42.4 

43-4 

44-6 

45-7 

46.8 

47-7 

48.7 

49-6 

.1844 

4.25 
4-50 

: 

_ 

39-6 
38-1 

40.2 
38-7 

40.4 
39-2 

41.0 
39-7 

41.8 
40.4 

41-6 

& 

46-3 
44.6 

47-o 
45-2 

47-6 
45-7 

•1959 

.-075   ; 

4-75 

- 

- 

36-6 

37-4 

37-6 

38.4 

39-i 

39-9 

41.0 

42.0 

42.8 

43-6 

44.2 

.2190 

5.00 

~ 

- 

.IS-' 

3.S-8 

36^2 

36.9 

37-8 

38-5 

39-3 

40.3 

41.1 

41.9 

42.6 

.2305 

5-25 

- 

- 

34-6 

35.2 

35-4 

35-9 

.37-0 

38.0 

37-7 

39-2 

39-o 

39-8 

.2422    i 

5-50 
6.00 

_ 

_ 

- 

33-o 
31.0 
28.8 

32.2 
30.6 

33-8 
32.1 

30-3 

34-5 
32-7 
31.0 

35-3 
33-6 
31-6 

36-3 
34-7 

32.3 

37-2 
35-2 

37-7 
35-6 
33-6 

37-4 

.2536 
.26^1 
.2766 

625 

~ 

- 

- 

27.4 

29.2 

28.1 

,o.S 

29.9 

- 

- 

31.1 

- 

- 

.2881 

6.50 

~ 

- 

24.1 

25.8 

27-3 

27-3 

27.7 

28.0 

28.2 

28.4 

28.6 

- 

- 

.2997 

6.75 

— 

— 

23.6 

— 

— 

26.1 

- 

— 

— 

.3112 

7.00 

- 

- 

lS.2 

20.8 

22.1 

22.5 

22.8 

23.0 

23.2 

24.0 

- 

- 

- 

.3228 

19-5 

19.9 

20.3 

20.5 

21.2 

•3343 

TABLE  125.  -  Secular  Variation  of  the  Horizontal  Intensity. 

Values  of  the  horizontal  intensity,  ff,  in  British  units,  for  stations  given  in  first  column  and  epochs  given  in  top  line. 
The  values  for  1890  and  1895  have  been  extrapolated  from  the  values  up  to  1885.  The  epochs  are  for  January  i  of 
the  different  years  given. 


Station. 

1840 

1845 

1850 

1855 

1860 

1865 

1870 

1875 

1880 

1885 

1890 

1895 

Cambridge    .    . 

3-66 

3-61 

3-S6 

3-S5 

3-S9 

3-62 

3-66 

3-68 

3-70 

3-71 

3-73 

3-74 

New  Haven  .     . 

3.80 

3-75 

3-70 

3-72 

3-76 

3*> 

3-83 

3.86 

3-87 

3-87 

3.86 

New  \  ork    .     . 

4.02 

4.01 

3-97 

3-93 

3-94 

3-97 

3-99 

4.01 

4-03 

4-o.s 

4.07 

Sandy  Hook 

4.09 

4.06 

3-92 

3-94 

3.98 

4.01 

4.04 

4.07 

4.10 

4.13 

4.16 

Albany     . 

3-6o 

3-58 

3-58 

3-58 

3-58 

3.60 

3.61 

3-63 

3-64 

3-66 

3-67 

3-69 

Philadelphia      . 

4-18 

4.1  S 

4.14 

4-13 

4-13 

4.14 

4.16 

4.19 

4.22 

4--v; 

4.24 

4.24 

Baltimore     •    . 
Washington 

ta 

+23 
4.26 

4.21 

4-25 

4.20 
4.26 

4.21 

4.21 

4-31 

4,22 
4-33 

4-  -4 
4-35 

4-25 
4-37 

4.27 

4-39 

4.28 
4,41 

4-3° 
4.42 

Toronto   .    .    . 

3-S6 

3-.S4 

3-53 

3-51 

MO 

3-49 

3-  So 

4-52 

3.56 

4.00 

4.61 

Cleveland     .    . 

4.00 

3-98 

3-97 

3-96 

3-96 

3-97 

3-98 

3-99 

4.01 

4-03 

4-05 

4.07 

Detroit     . 
San  Diego    .     . 

3-91 

6.12 

3-89 
6.19 

3.86 

6.22 

£l 

tfl 

,.86 
6.24 

3-87 

6.20 

3-89 
6.1  S 

3-90 
6.10 

3-9^ 
6.07 

3-93 
6.04 

0.03 

Santa  Barbara  . 

S.87 

S-93 

S-94 

5-95 

S-96 

S-9S 

5-94 

S-92 

$48 

5*4 

5-77 

Monterey 

.S-63 

5-77 

5-76 

5-75 

5-72 

5-69 

5-66 

5-65 

5.64 

5-63 

San  Francisco  . 

5-49 

5-54 

5-50 

5-57 

5-59 

5-59 

5-58 

5-54 

5-49 

5-47 

5-45 

Fort  Vancouver 

4-44 

4-51 

4-55 

4-56 

4.58 

4-58 

4-57 

4.56 

4-54 

4-53 

4-5-     4-5- 

SMITHSONIAN  TABLES. 


112 


TERRESTRIAL    MAGNETISM. 


TABLE  126. 


Secular  Variation  ol  Doollnatlon  In  the  Form  of  a  Function  ol  the  Time  lor  a  Number  ol  Station* 

Moivi-xir,,,|,.,l  t.il.lp  will  be  fo.m.liM  App.  /,- •  U,,ii,.,|  Stairs  (',,.,-,,  .„„!  ( .,,,,|,,ic  Survey  Report  for  1X88,  from 

wlni-li  tins  ul.lr  IMS  b«:,.,.  compiled.     Tile  v.iri.il,l,-  „,  is  ,, -,  I, ,|  I,,,,,,  .!„•  ,,„„  I,   ,HSo  ami  thus™/  -  1850. 


Station. 

Latitude. 

l.mx.itud,-. 

The  magnetic  declination  (/>)  expreued  as 
a  function  of  time. 

(a) 

Eastern  Series  of  Stations. 

0          / 

0         / 

00                                                         0 

St.  Johns,  N.  F  
Quebec,  Canada  .        ,        »        . 

47  34-4 
46  48.4 

S24I.9 

71  '4-5 

21.944-    8.89  sin  (1.05  m  4-63.4)* 
14.66-1-    3.03  sin  J  i.  4  »/    --    4.6) 

Charlottetown,  P.  E.  I.       .     .   . 
Montreal,  Canada      .        .        . 

46  14.0 
45  30-5 

63  27.0 
73  34-6 

4-    0.61  sin  (4.0  m    -j-    0.3) 

15-95-f-    7*7&ffo.(I.9M    +49-8) 
1  1.88  -f-    4.17  sin  (i.  5  m   —18.5) 

44  82.2 
44  39.6 

68  46.9 
63  35-3 

-    0.36  sin  (4.9  m    -j-  19.0) 
13.86  -f    3.55  sin  (1.30  m  4-    8.6) 
16.184-    4.53  sin  ([.oo  w  4  46.1  * 

Halifax,  N.  S.      .          .          .        -. 

Albany,  N.  Y  
Cambridge,  Mass.       .        . 

42  39  2 
42  22.9 

73  45-8 
71  07.7 

8.  1  7  -j-    3-02  sin  (1.44  m  —  8.3 
9.54  4    2.69  sin  (1.30  m  4-    7.0) 

Q 

4-    0.18  sin  (3.20  m  -\-  44.0) 

New  Haven,  Conn.     .        .        . 
New  York,  N.  Y. 

41  18.5 

40  42.7 

72  55-7 
7400.4 

7-78  -f    3-1  1  sin  (1-40  w  —  22.1) 
7.044-    2.77  sin  (1.30m  —  18.1) 

I  l.nrisburg,  Pa.  .         .        .        ; 
Philadelphia,  Pa. 

40  15.9 
39  5&-9 

70  52-6 
75  09-0 

-f-    0.14  sin  (6.30  m  4-  64.0 
2.93  -f-    2.98  sin  (1.50  ;//  -j-    0.2 
5-364-    3-17  sin  (1.50  ;//  —  26.1 

4-    0.19  sin  (4.00  m  -|-  M-6 

Washington,  I).  C.     , 

38  53*3 

7700.6 

2-73  -f    2.57  sin  (1.45  ;;/  —  21.6) 

4-    0.14  sin  (12.00  m  4  27) 

<  .i|>e  Henry,  Va.         .        ... 
Charleston,  S.  C.        .      .,.        t 

36  55-6 
32  46.6 

76  00.4 
70  55-8 

2.424-    2.25  sin  (1.47  ni  —  30.6) 
—  1.82-j-    2.75  sin  (1.40  //;  —  12.1)* 

Paris,  P>ance       .... 

48  50.2 

t  2  20.2 

6.4794-  16.002  sin  (0.765  m  4  1  18.77) 

4  [0.85—  0.35  sin  (O/HV/M  sin  [(4.04 

St.  Cicorge's  Town,  Bermuda 
Rio  de  Janeiro,  Brazil         .        . 

32  23.0 

—22  54.8 

64  42.0 
4309.5 

+  0.0054  ;/  -f  .000035  «-);/]  \ 
6.95  4-  0.0145  ;;/  4-  0.00056  in1  * 
2.19  4-  9-91  sin  (0.80  m  —  10.4)* 

(d)  Central  Series  of  Stations. 

York  Factory,  R  N.  A. 

I'ort  Albany,  H.  N.  A. 

56  59-9 

52  22.O 

92  26.O 
82  38.0 

7.34  +16.03  sin  (i.  low  —  97.9) 
1  5-78  4-  6.95  sin  (  \  .20  m  —  99.6  * 

Sanli  Sie  Marie,  Mich. 
Toronto,  Canada        .        .        . 

46  29.9 

43  39-4 

84  20.  1 

79  23-5 

1-544-  2.70  sin  (1.45  m  —  58.5 
3.60  4-  2.82  sin  (1.40  m  —  44-7) 

•j-  0.09  sin  (9.30  ;//  4  '  36) 

4-  0.08  sin  (19.00  in  4-  247) 

Chicago,  Til.        .... 
Cleveland.  Ohio           .        .        . 

41  50.0 
41  30.4 

87  36.8 
81  41.5 

—    377+  2.48  sin  (  i.  45  w  —  62.5 
0.47  4-  2.39  sin  (1.30  m  —  14.8) 

1  )enver,  Colo.      •        «     ^  .        . 

39  45-3 

104  59-5 

—  I5-3°  T  o.oi  i  m  -f-  0.0005  in* 

Athens,  <  )hio        ,         .      "  ,          . 

39  '9-° 

82  O2.O 

—    1.51  4~  2.63  sin  (1.40  w  —  24.7) 

Cincinnati,  Ohio          ..         .         . 

3008.4 

84  25-3 

—    2.59  4-  2.43  sin  (1.42  m  —  37.9) 

St.  1  ,onis,  Mo.     .         .         *         « 

3»  38.0 

90  12.2 

—    5.91  4-  3-00  sin  (1.40  »*  —  51.1)* 

New  (  >i  leans.  La. 

29  52-2 

90  03.9 

—    5.20  -f  2.98  sin  (  1.40  m  —  09.8) 

Key   West,  Fla  

Kingston,  Port  Royal,  Jamaica  . 

24  33-5 
17  55-9 

81  48.5 
76  50.0 

—   4.31  4  2.86  sin  (1.30  M  —  23.9) 
—    381+  2.39  sin  (i.  10  m  —  10.6) 

(t>)  Stations  on  the  Pacific  Coast,  etc. 

City  of  Mexico,  Mex. 

19  26.0 

99  1  1.6 

—    5-34  +  3-28  sin  (  i.  oo  m  —   87.9)* 

('eii-os  Island,  Lower  Cal.,  Mex. 

28  04.0 

115  I2.O 

—    7.40  4-  4.61  sin  (1.05  ///  —  107.0) 

San  Francisco,  Cal.     .        .        . 

37  47-5 

122  27.3 

—  1  3.94  4-  2.65  sin  (1.05*1  —  J35-5) 

Vancouver,  Wash.       .         .         . 

45  37-5 

122397 

—  17-93  +  3  I2  sin  (1.35  m—  134.1) 

Sitka.  Alaska        .          .          .          . 
Port   Etches,  Alaska    . 

57  02.9 
60  20.7 

135  '9-7 
146  37.6 

—  215.79  +  3.30  Bin  (i-3o»/  —  ro'.2) 
—  23.7  1  4-  7-Jty  sin  iI-3S  M  —   <s°-9) 

Pctropavlovsk,  Siberia 

53  01.0 

tis8  43.0 

—   3-35  4-  2.97  sin  (1.30^  4-    12.2) 

i   Compiled  h..m 

stanl  ;nul  first   pi-riodii:  tc 
wave  «  rr  /  —  i  ,-o. . 

SMITHSONIAN   TABLES. 


si.in.  t  East  longitude. 

•ic-s  of  .ihscrv.itions  i-xtendinR  back  to  1541.     The  primary  wave  follows  the  sum  of  the  ron- 

srm  closely.     The  period  seems  to  be  about  470  years.     In  the  expression  for  the  secondary 


1 1.3 


TABLE  127. 


TERRESTRIAL    MAGNETISM. 

Secular  Variation  of  the  Declination.  —  Eastern  Stations.4 


•  •.     .           

Station. 

1800 

1810 

1820 

1830 

1840 

1850 

1860 

1870 

1880 

1890 

1900 

0 

o 

o 

o 

o 

o 

0 

o 

o 

o 

o 

St.  Johns,  N.  F.  .     . 
Quebec,  Canada  .     . 

23-5 

12.1 

25.0 

I2.I 

26.5 

12.3 

28.0 
12.9 

29.0 

13-8 

29.9 
14.9 

35-o 
16.0 

30.8 

16.9 

30.8 
17.4 

30-5 

*7'S 

29.9 

17-5 

Charlottetown, 

P.  E.  I  

- 

- 

- 

J9-3 

20.7 

21.9 

22.8 

234 

23.7 

23-7 

23-3 

Montreal,  Canada     . 
Eastport,  Me.  .     .     . 

8.0 
13.2 

7.8 
I4.O 

7-9 
14.8 

8.4 
15.6 

94 

16.4 

10.7 
17.1 

I2.O 

I7.8 

13.0 

18.3 

13.8 

18.7 

14.4 
18.9 

15.0 

19.0 

Bangor,  Me.     .     .     . 

10.9 

11.4 

I2.I 

12.8 

13.6 

14.4 

15.2 

15-9 

16.5 

16.9 

17-3 

Halifax,  N.  S.  .     .     . 

15-9 

16.7 

174 

18.2 

18.9 

19.4 

19.9 

20.3 

2O.6 

20.7 

20.7 

Burlington,  Vt.     .     . 

7-3 

7-2 

7-5 

8.1 

8.9 

H 

10-3 

I  I.O 

11.9 

12.8 

J3-5 

Hanover,  N.  H.  .     . 

5-8 

6.0 

6-5 

7.2 

7-9 

8.8 

9.8 

10.8 

11.7 

12.5 

13-1 

Portland,  Me.  .     .     . 

8.5 

8.9 

9-5 

IO.I 

10.8 

11.6 

I2.3 

13.0 

13.6 

14.1 

14.4 

Rutland,  Vt.    .     .     . 

6-3 

6.2 

6.5 

6.9 

7.6 

8.5 

9.4 

10.4 

"•3 

12.3 

13.0 

Portsmouth,  N.  H.  . 

74 

7-7 

8.1 

8.7 

9-5 

10.3 

II.  I 

fi.9 

12.7 

!3-3 

13-7 

Chesterfield,  N.  H.  . 

6.0 

6.4 

7.0 

7-7 

8.5 

94 

10.3 

II.  2 

I2.O 

12.6 

Newburyport,  Mass. 

7-3 

7.6 

8.1 

8.6 

9-3 

IO.O 

10.7 

11.4 

12.0 

I2.5 

12.8 

Williamstown,  Mass. 

5-7 

5-9 

6-3 

6.8 

7-4 

8.1 

8.8 

9.6 

10.3 

IO-9 

11.4 

Albany,  N.  Y.      .     . 

_ 

5-4 

5.8 

6-3 

7.0 

7-7 

8.5 

9.2 

9.9 

I0.5 

10.9 

Salem,  Mass.   .     .     . 

6-3 

6.6 

7.2 

7-9 

8.7 

9.6 

10.6 

11A 

.12-3 

13.5 

Oxford,  N.  Y.  .     .     . 

3-° 

3-1 

3-4 

3-9 

4-5 

5-i 

5-9 

6.6 

74 

o.O 

8.6 

Cambridge,  Mass.    . 

7-1 

7-5 

8.0 

8.6 

9-3 

IO.O 

10.6 

II.  2 

n.6 

11.9 

12.0 

Boston,  Mass.  .     .     . 

6.9 

7-3 

7.8 

8.4 

9.0 

9-7 

10.3 

IO-9 

M-5 

11.9 

12.2 

Provincetown,  Mass. 

7.2 

7-7 

8.2 

8.9 

9.6 

10.2 

10.9 

H'5 

I2.O 

12.4 

12.6 

Providence,  R.  I.  .     . 

6-5 

6-5 

6.7 

7-3 

8.2 

9.2 

9.8 

IO.2 

10.8 

11.6 

I2.I 

Hartford,  Conn.  .     . 

S-2 

S-2 

5-5 

5.8 

6.2 

6.8 

74 

8.0 

8.6 

9.2 

9.8 

New  Haven,  Conn.  . 

4-7 

4-7 

5-° 

5-4 

5-9 

6.6 

7-3 

8.1 

8.8 

9-5 

IO.I 

Nantucket,  Mass. 

6.8 

7-2 

7-7 

8.7 

9.0 

9.6 

IO.I 

10.6 

I  I.O 

ii-3 

11.5 

Cold  Spring  Harbor, 

N.  Y  

4-7 

4-9 

S-2 

5-6 

6.1 

6.7 

7-3 

7-9 

8.4 

8.9 

9-3 

New  York,  N.  Y.     . 

4-3 

4-5 

4-6 

5-° 

5.6 

6-3 

6.9 

74 

7-9 

8.5 

9.1 

Bethlehem,  Pa.    .     . 

2.6 

2-3 

2-3 

2-5 

2.9 

3-5 

4.2 

5-° 

5.8 

6.7 

74 

Huntingdon,  Pa.  .     . 

I.O 

0.8 

0.9 

i.i 

i-5 

2.1 

2.7 

3-5 

4.2 

4.9 

5.6 

New  Brunswick, 

N   T 

2.C 

2.Q 

•J.A 

4.0 

4.7 

c.-j 

6.0 

6.6 

7.1 

7*^ 

7.Q 

Jamesburg,  N.  J.  .     . 
Harrisburg,  Pa.    .     . 

j 

3-i 

0.0 

**5f 

3-i 
o-3 

J  T- 

3-4 
0.8 

If-.W 

3-8 
1.4 

T-  / 

4-3 

2.2 

JO 

4.9 
2.9 

5.6 

3-7 

6-3 
44 

/ 

7-0 

5-o 

/    D 

7.6 

5-5 

/    -/ 

8.2 

5-8 

Hatboro,  Pa.    ... 

1.8 

2.O 

2-5 

3-° 

3-7 

4-3 

5-° 

5-7 

6.7 

8.0 

Philadelphia,  Pa.      . 

2.1 

2.2 

2.4 

2.9 

3-4 

4.1 

4-7 

54 

6.2 

7.0 

7-7 

Chambersburg,  Pa.  . 

-0-3 

—0-5 

—0-3 

0.2 

0.7 

1.4 

2.0 

2-7 

34 

4.2 

5-° 

Baltimore,  Md.     .     . 

0.6 

0.7 

0.9 

1.2 

1-7 

•*>   "» 

2.9 

3-5 

4.2 

4-7 

5-2 

Washington,  D.  C.  . 

0.2 

0.2 

0.4 

0.7 

i.i 

i'i 

2-5 

2.9 

3-7 

4-3 

4.6 

Cape  Henlopen,  Del. 

0.8 

0-9 

i.i 

i'S 

2.O 

2.6 

2.4 

4.1 

4-9 

5-6 

6.2 

Williamsburg,  Va.     . 

—  O.2 

—0-3 

—0.2 

0.0 

0.4 

0.9 

1.5 

2.1 

2-7 

3-3 

3-9 

Cape  Henry,  Va.  .     . 

0.2 

0.2 

0.2 

°-5 

0.8 

i-3 

1.8 

2.4 

2.9 

3-5 

3-9 

New  Berne,  N.  C.     . 

—1.9 

—1-9 

—1.6 

T       ^ 

—o-7 

—  0.2 

o-5 

I.I 

i-7 

2-3 

2-7 

Milledgeville,  Ga.     . 

—5-0 

—5-3 

-5.6 

-5-6 

—5-5 

—5-3 

—  5-° 

-4-5 

—4.0 

-34 

—2.7 

Charleston,  S.  C.      . 

—4-5 

—4.4 

—4.0 

-3-6 

—  3-o 

—2.4 

—i-7 

—  i.i 

—0.4 

O.I 

o-5 

Savannah,  Ga.      .     . 

—4-7 

—4-7 

—4.2 

-3-8 

—3-3 

—2.7 

—  2.1 

—1.4 

—0.9 

Paris,  France  .     .    . 

22.6 

22.3 

21.9 

21.8 

21.8 

20.9 

19.1 

«7-S 

16.6 

IS-1 

St.  George's  Town, 

B  I      

_ 

— 



60 

60 

6  o 

7T 

7  C 

7  Q 

81 

Rio  de  Janeiro,  Bra- 

u.y 

u.y 

u.y 

-1 

/•J 

/•y 

(7«<| 

zil    

—5-4 

—4-5 

—3-4 

—  2.2 

—0.9 

0.4 

1.8 

3-1 

4-5 

5-8 

*  This  table  gives  the  secular  variation  of  the  declination  since  the  year  1800  for  a  series  of  stations  in  the  Eastern 
States  and  adjacent  countries.  Compiled  from  a  paper  by  Mr.  Schott,  forming  App.  7,  Report  of  the  United  States 
Coast  and  Geodetic  Survey  for  1888.  The  minus  sign  indicates  eastern  declination. 

SMITHSONIAN  TABLES. 

114 


TERRESTRIAL    MAGNETISM. 

Secular  Variation  of  the  Declination.  —  Central  Stations.* 


TABLE  1 28, 


Station. 

1800 

1810 

1820 

1830 

1840 

1850 

1860 

1870 

1880 

1890 

1900 

York  Factory,  Brit. 

, 

N  A      . 

O.] 

—  ?  c 

A    1 

f.   r 

Q 

o  ., 

O   £ 

o  ^ 

^ 

_    S 

Fort  Albany,  Brit. 

• 

4-7 

—  °-5 

~7' 

—  o.  c 

—  o.o 

—7.2 

—5-° 

—  3-6 

N.  A.     .     .•    .     . 

I  ^  A 

12.1 

I  O.C 

I  O.O 

_ 

Q  0 

0  0 

r\  £\ 

Duluth,  Minn.   . 

( 

9-3 

5-9 

o.o 

9.1 

9.0 

10.3 

11.4 

Superior  City,  Wis. 

r 

~ 

~~ 

~" 

— 

-9.8 

—  IO.O 

—  IO.I 

—  IO.I 

—9.9 

-9-5 

Sault    Ste.    Marie, 

Mich 

—  O.  ' 

o.c 

T      1 

T     < 

r>  R 

_    0 

™  ^J  «U 

—  i.o 

—  O.O 

°-3 

O.2 

O.o 

I.C 

2.2 

Pierrepont   Manor, 

N.  Y      . 

2.6 

i  r> 

d_ 

0  0 

0   Q 

Toronto,  Canada    . 

'_ 

_ 

3-° 
0.8 

3-7 

4-5 
1.6 

54 

2.2 

j 
2-7 

7.2 

O.O 

4.1 

O.O 

4.8 

Grand  Haven,  Mich. 
Milwaukee,  Wis.    . 
Buffalo,  N.  Y.    .     . 

O.2 

0.2 

0.4 

—5-2 
0.8 

—5-2 

—4.9 
—74 

2.O 

—44 
-6.0 

2.8 

3-7 

2.7 
—54 
4-5 

T-* 

—4-5 

5-3 

*t*^ 

Detroit,  Mich.   .     . 

—3-2 

—  3-1 

—2.9 

—2-5 

—  2.1 

—1.6 

—  I.O 

—  0.4 

O.I 

0.6 

0.9 

Ypsilanti,  Mich.     . 

—4.1 

—3-6 

—  3-° 

—  2.2 

—1.4 

—0.6 

O.2 

0.9 

1.5 

1.9 

Erie,  Pa  

—  °*5 

—0.5 

—  o./ 

—  O.I 

0.4 

0.9 

1.6 

2-2 

3.0 

3-6 

4.2 

Chicago,  111.  .     .     . 
Michigan  City,  Ind. 

- 

~~ 

—6.2 

-6-3 
-5-6 

—6.2 

—54 

—6.0 

—  5-° 

—  5-1 
—4.0 

-4.6 

—3-5 

—4.0 
—2.9 

—3-3 
—2.3 

Cleveland,  Ohio     . 

J     Q 

J  7 

—  I   ^ 

—i.i 

—0.6 

—  O.I 

0.4 

0.9 

1.4 

1.9 

2.T. 

Omaha,  Neb.     .     . 

- 

—  12.5 

—  12.( 

—  12.6 

—12.4 

—  I2.O 

—  u-5 

—10.9 

—  IO.2 

—  9-5 

-8.7 

Beaver,  Penn.    . 

I.I 

—  I." 

—  I.' 

—  i.i 

—0.8 

—  O.I 

O.2 

0.9 

1.5 

2.2 

2.8 

Pittsburg,  Pa.    .     . 

- 

- 

- 

- 

0.2 

0.7 

I.I 

1.9 

2.C 

3-1 

3-5 

Denver,  Colo.    .     . 

~ 

— 

- 

- 

— 

—  I5.I 

—14.9 

—14-5 

—14.1 

Marietta,  Ohio  .     . 

_ 

—  2.9 

—2.8 

—2-7 

—2-3 

""•"I  .Cj 

—  1-3 

—0.6 

O.I 

0.8 

1.4 

Athens,  Ohio     .     . 

—  4.1 

—4.1 

—3-9 

—3-6 

—  3-1 

—2.6 

2.0 

—  14 

—0-7 

—  O.I 

0.4 

Cincinnati,  Ohio    . 
St.  Louis,  Mo.   .     . 

—4-9 

—5-0 

—5-0 

-4.8 
-8.9 

—4-5 
—8.6 

—4.1 

—8.2 

-3-6 

—7-7 

—3.0 

—7-i 

—2.4 
-6.4 

—1.8 
—5-6 

—1-3 

Nashville,  Tenn.    . 

- 

- 

-6.7 

—6.9 

-6.9 

-6.7 

—6-3 

-5-8 

—  5-1 

—44 

—  3-6 

Florence,  Ala.   .     . 
Mobile,  Ala.  .     .     . 

-5.8 

—6.5 
-6-3 

3! 

—6-5 
—7-o 

-6.4 
—7-1 

—6.1 

—7.0 

=8 

l£3 

-4.8 
-5-8 

—4-3 

-3* 

—4.6 

Pensacola,  Fla.  .     . 
New  Orleans,  La.  . 

—  7-1 

—7.2 
-7.6 

-7.6 
—8.1 

—  8.0 

—6.6 

—7-7 

—  6'.o 

—7.2 

—6.6 

I** 

-3-8 

—5-2 

San  Antonio,  Texas 

—9.8 

—  IO.I 

—10.3 

—  IO.2 

—  IO.I 

—9-7 

—9-3 

—8.7 

-8.1 

Key  West,  Fla.      . 

_ 

_ 

-6.9 

-6.5 

-6.0 

—5-5 

-4.8 

—4.2 

-3-6 

—  3-° 

—  2.4 

Havana,  Cuba  .     . 

—7.0 

-6.9 

—6.6 

-6-3 

-5-8 

—5-3 

-4.8 

—4.2 

-3-6 

—2-5 

Kingston,  Port 

Royal,  Jamaica  . 

—6.0 

-5.8 

—5-5 

—  5-i 

—4-7 

—4-3 

-3-8 

—3-3 

—2.9 

—2-5 

—  2.1 

Barbadoes,  Car.  Isl. 

—34 

—3-0 

-2-5 

—  2.0 

—  1.5 

—  0.9 

—0.4 

O.I 

°-5 

0.9 

1.2 

Panama,  New  Gra- 

nada     .... 

—7-9 

-7.8 

-7.6 

—7-3 

—7.0 

-6.7 

-6-3 

—5-9 

—5-5 

—  5-° 

-4.6 

*  This  table  gives  the  secular  variation  of  the  declination  since  the  year  1800  for  a  series  of  stations  in  the  Central 
States  and  adjacent  countries.     The  minus  sign  indicates  eastern  declination.     Reference  same  as  Table  127. 

SMITHSONIAN  TABLES. 

us 


TABLE  129. 


TERRESTRIAL    MAGNETISM. 

Secular  Variation  of  the  Declination.  —  Western  Stations.* 


Station. 

1800 

1810 

1820 

1830 

1840 

1850 

1860 

1870 

1880 

1890 

1900 

0 

o 

0 

0 

0 

o 

0 

0 

o 

o 

o 

Acapulco,  Mex  

7.6 

8.1 

8  s 

8.7 

8.9 

8.9 

8.7 

8.5 

8.1 

7  6 

7  I 

Vera  Cruz,  Mex  

8.6 

9.0 

9-3 

*/ 

9-3 

*~».^/ 

9.2 

si 

aj 

7.0 

/  *" 

6.2 

/  * 

5-3 

City  of  Mexico,  Mex.     .     . 

7-5 

7-9 

8.5 

8.6 

8.6 

8.5 

8.4 

8.1 

7.8 

74 

San  Bias,  Mex  
Cape  San  Lucas,  Mex.  .     . 

7.8 
6.9 

84 
7.6 

8.9 
8-3 

& 

9.4 
9.2 

94 
9-5 

9-3 
9.6 

9.0 
9.6 

8.5 

94 

7-9 
9.0 

Magdalen  a  Bay,  L.  Cal.     . 

6.6 

74 

8.2 

8.9 

9-5 

IO.O 

10.3 

10.5 

10.5 

10.3 

IO.O 

Ceros  Island,  Mex.   .     .     . 

9.0 

9.8 

10.5 

II.O 

11.8 

I2.O 

12.0 

11.9 

1  1.  6 

II.  2 

El  Paso,  Mex  





12.3 

12.5 

12.4, 

12.7 

1  1.9 

lid 

San  Diego  Cal  

10.8 

1  1  A. 

II.9 

12  7 

127 

17  O 

X  *.«£J. 

172 

J 

177 

i  i.q. 

Santa  Barbara,  Cal.  .     .     . 

ii!6 

12.3 

i  i.i|. 
I2.9 

134 

i  .£.  j 
13-9 

i  *../ 
14-3 

Ij.U 

14.6 

1  j'* 
I4.8 

O'J 

14.8 

[4! 

14.6 

Monterey,  Cal  

12.3 

12.9 

134 

J3-9 

144 

14.9 

15.3 

1  6.6 

!5-9 

16.0 

16.1 

San  Francisco,  Cal.  .     .    . 
Cape  Mendocino  .... 

13.6 

14.1 
15.6 

1  6.0 

16.5 

154 
16.9 

I5.8 

17.2 

16.1 

17.4 

16.3 
17.6 

16.5 
17.7 

16.6 

17.7 

1  6.6 
17.6 

Salt  Lake  City,  Utah     .     . 

_ 

_ 

_ 

— 

16.0 

16.4 

1  6.6 

1  6.6 

16.3 

Vancouver,  Wash.    .     .     . 

16.8 

'/•S 

18.2 

18.9 

19.6 

20.2 

20.6 

20.9 

21.0 

21.0 

20^8 

Walla  Walla,  Wash.     .    . 

_ 

_ 

_ 

_ 

_ 

204 

20.8 

2I.O 

21.  1 

21.  0 

20.8 

Cape  Disappointment, 

Wash  

17.7 

18.2 

187 

T  n  ? 

IQ.8 

"2O     1 

2O.8 

21.2 

21.6 

21.8 

T  n 

Seattle,  Duwanish  Bay, 

1  /•/ 

HJ./ 

»3T** 

' 

" 

Wash 

1  T    1 

21.8 

^2  I 

_  _     _ 

22.2 

22.1 

Port  Townsend,  Wash.      . 

18.1 

18.8 

19.6 

20-3 

20.9 

21  4 

21.7 

21.8 

21.8 

21-5 

21.  1 

Nee-ah  Bay,  Wash.  .     .     . 

18.3 

18.9 

19.6 

20-3 

2I.O 

21.6 

22.1 

22.5 

22.7 

22-7 

22.6 

Nootka,  Vancouver  Island 

19.6 

20.  i 

20.7 

21.3 

22.0 

22.5 

23.0 

23-5 

23.8 

23-9 

24.0 

Captain's  and  Iliuliuk  Har- 

bors, Unilaska  Island    . 

19-3 

19.6 

19.7 

19.8 

197 

19.7 

19-5 

19-3 

18.9 

18.6 

18.2 

Sitka,  Alaska   

26.4 

•77    T 

27.8 

28.3 

28.7 

29.1 

28.8 

^C        A 

^7  O 

St.  Paul,  Kadiak  Island     . 
Port  Mulgrave,  Yakutat 

25-5 

l/.l 
26.4 

27.0 

27-3 

274 

27.1 

26.6 

25-9 

25.0 

23-9 

22.7 

Bay,  Alaska  

278 

2O  2 

7O  A 

71.2 

71  7 

31.8 

71  A 

7O  7 

2O  7 

28.4 

26.8 

Z./.U 

y- 

6  4 

J1'/ 

J    4 

J    V 

y-/ 

Port  Etches,  Alaska  .     .     . 

27.8 

29-3 

3°4 

31.2 

3T.6 

31  5 

31.0 

30.1 

28.8 

27-3 

25-S 

Port  Clarence,  Alaska  .     . 

26.6 

27.0 

26.9 

264 

25.6 

244 

22.9 

21.2 

Chamisso    Island,    Kotze- 

bue  Sound 

11    T 

711 

2Q.6 

^0 

26.8 

•7C   "> 

'>'?   C 

Petropavlovsk,  Kamchatka, 

J1'1 

'3 

***• 

5- 

-3-5 

Siberia      

c  7 

C  2 

A   7 

4T 

7  A 

2  7 

2.1 

T    C 

I.O 

O  7 

n  c 

ft 

.1 

*••/ 

w./ 

*  This  table  gives  the  secular  variation  of  the  declination  since  the  year  1800  for  a  series  of  stations  in  the  Western 
States  and  adjacent  countries.    The  declinations  are  all  east  of  north.     Reference  same  as  Table  127. 


SMITHSONIAN  TABLES. 


116 


TABLE  130. 


TERRESTRIAL    MAGNETISM, 


Agonic  Lines.4 


The  line  of  no  declination  is  moving  westward  in  the  United  States, 
and  east  declination  is  decreasing  west  of,  while  west  declination  is 
increasing  east  of  the  agonic  line. 


Lat.  N. 

Longitudes  of  the  agonic  line  for  the  years  — 

1800 

1850 

1875 

1890 

o 

o 

o 

o 

o 

25 

- 

- 

- 

75-5 

30 

- 

- 

- 

78.6 

35 

_ 

76.7 

79.0 

79-9 

6 

75.2 

77-3 

79-7 

80.5 

7 

76.3 

77-7 

80.6 

82.2 

8 

76.7 

78.3 

81.3 

82.6 

9 

76.9 

78.7 

81.6 

82.2 

40 

77.0 

79-3 

81.6 

82.7 

i 

77-9 

80.4 

81.8 

82.8 

2 

79.1 

81.0 

82.6 

837 

3 

794 

81.2 

83.1 

84-3 

4 

79.8 

- 

83-3 

84.9 

45 

_ 

_ 

83.6 

85.2 

6 

_ 

- 

84.2 

84.8 

7 

- 

- 

85.1 

85-4 

8 

_ 

- 

86.0 

85-9 

9 

— 

*• 

86.5 

86.3 

*  Reference  same  as  Table  127. 
SMITHSONIAN  TABLES. 

u; 


TABLE  131 . 


TERRESTRIAL   MAGNETISM. 


Date  of  Maximum  East  Declination.* 


This  table  gives  the  date  of  maximum  east  declination  for  a  number  of 
stations,  beginning  at  the  northeast  of  the  United  States  and  ex- 
tending down  the  Atlantic  coast  to  New  York  and  west  to  the  Pacific. 


Station. 

Date. 

Halifax,t  N.  S.        .        .        .        .    ; 

1714 

Eastport,  Me.          .... 

1753 

Bangor,  Me  

1774 

Portland,  Me.          .... 

1779 

1780 

New  Haven,  Conn. 

1800 

New  York,  N.  Y  

1784 

Jamesburg,  N.  J  

1802 

Philadelphia,  Pa  

1802 

Pittsburg,  Pa  

1808 

Cincinnati,  Ohio      .... 

1814 

Florence,  Ala.         .... 

1821 

1822 

Nashville,  Tenn  

1834 

Chicago,  111  

iS""! 

Denver,  Colo.          .... 

1839 

Salt  Lake,  Utah      .... 

1873 

Vancouver,  Wash. 

1883 

Cape  Mendocino,  Cal.     . 

1886 

San  Francisco,  Cal. 

1893 

*  Reference  same  as  Table  127. 

t  The  opposite  phase  of  maximum  west  declination  is  now  located 
at  Halifax. 

SMITHSONIAN  TABLES. 


118 


TABLE   132, 


PRESSURE    OF   COLUMNS    OF    MERCURY   AND   WATER. 

British  and  metric  measures.     Correct  at  o°  C.  for  mercury  and  at  4°  C.  for  water. 


METRIC  MEASURE. 

BRITISH  MEASURE. 

Cms.  of 
Hg. 

Pressure 
in  grammes  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

Inches  of 
Hg. 

Pressure 
in  grammes  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

1 

I3-5956 

0.193376 

1 

34-533 

0.491174 

2 

27.1912 

0.386752 

2 

69.066 

0.982348 

3 

40.7868 

0.580128 

3 

103.598 

1.473522 

4 

54-3824 

0.773504 

4 

I#.i3l 

1.964696 

5 

67.9780 

0.966880 

5 

172.664 

2.455870 

6 

81.5736 

1.160256 

6 

207.197 

2.947044 

7 

95.1692 

I-353632 

7 

241.730 

3.438218 

8 

108.7648 

1.547008 

8 

276.262 

3.929392 

9 

122.3604 

1.740384 

9 

310.795 

4.420566 

10 

I35-9560 

1.933760 

10 

345-328 

4.911740 

Cms.  of 
H,O. 

Pressure 
in  grammes  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

Inches  of 
H2O. 

Pressure 
in  grammes  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

1 

I 

0.0142234 

1 

2-54 

0.036227 

2 

2 

0.0284468 

2 

5.08 

0.072255 

3 

3 

0.0426702 

3 

7.62 

0.108382 

4 

4 

0.0568936 

4 

10.16 

0.144510 

5 

5 

0.0711170 

5 

12.70 

0.180637 

6 

6 

0.0853404 

6 

15.24 

0.216764 

7 

7 

0.0995658 

7 

17.78 

0.252892 

8 

8 

0.1137872 

8 

20.32 

0.289019 

9 

9 

O.I280I06 

9 

22.86 

0.325147 

10 

10 

0.1422340 

10 

25.40 

0.361274 

SMITHSONIAN  TABLES. 


119 


TABLE  133. 

REDUCTION  OF  BAROMETRIC  HEIGHT  TO   STANDARD   TEMPERATURE.* 


Corrections  for  brass  scale  and 
English  measure. 

Corrections  for  brass  scale  and 
metric  measure. 

Corrections  for  glass  scale  and 
metric  measure. 

Height  of 
barometer  in 

a 

in  inches  for 

Height  of 
barometer  in 

a 

in  mm.  for 

Height  of 
barometer  in 

a 

in  mm.  for 

inches. 

temp.  F. 

mm. 

temp.  C. 

mm. 

temp.  C. 

15.0 

0.00135 

400 

0.0651 

50 

0.0086 

1  6.0 

.00145 

410 

.0668 

100 

.0172 

17.0 

.00154 

420 

.0684 

150 

.0258 

»7-5 

.00158 

43° 

.0700 

200 

•°345 

18.0 

.00163 

440 

.0716 

250 

.0431 

18.5 

.00167 

450 

.0732 

300 

.0517 

19.0 

.00172 

460 

.0749 

350 

.0603 

!9-5 

.00176 

470 

.0765 

480 

.0781 

400 

0.0689 

200 

O.OOlSl 

49° 

.0797 

45° 

•0775 

20.5 

.00185 

500 

.0861 

2I.O 

.00190 

500 

0.0813 

520 

.0898 

21-5 

.00194 

510 

.0830 

540 

•0934 

22.0 

.00199 

520 

.0846 

560 

.0971 

22.5 

.00203 

530 

.0862 

580 

.1007 

23.0 

.OO2O5 

540 

.0878 

23-5 

.00212 

550 

.0894 

600 

0.1034 

560 

.0911 

610 

.1051 

24.0 

0.00217 

570 

.0927 

620 

.1068 

24-5 

.00221 

580 

•0943 

630 

.1085 

25.0 

.OO226 

590 

•0959 

640 

.1103 

25-5 
26.0 

.00231 
.00236 

600 

0.0975 

6  so 
660 

.II2O 
•1137 

26.5 

.OO24O 

610 

.0992 

27.0 

.00245 

620 

.1008 

670 

0.1154 

27-5 

.00249 

630 

.1024 

680 

.1172 

640 

.1040 

690 

.1189 

28.0 

0.00254 

650 

.1056 

700 

.I2O6 

28.5 

.00258 

660 

.1073 

710 

.1223 

29.0 

.00263 

670 

.1089 

720 

.1240 

29.2 

.00265 

680 

.1105 

730 

.1258 

29.4 

.00267 

690 

.1121 

29.6 

.00268 

740 

0.1275 

29.8 

.00270 

700 

O.II37 

75° 

.1292 

30.0 

.OO272 

710 

•"54 

760 

.1309 

720 

.1170 

770 

•I327 

30.2 

0.00274 

73° 

.1186 

780 

•1344 

3°-4 

.00276 

740 

.1202 

790 

.1361 

30.6 

.00277 

750 

.1218 

800 

.1378 

30.8 

.00279 

760 

•I235 

31.0 
31.2 

.OO28l 
.00283 

770 
780 

.1251 
.1267 

850 

900 

0.1464 

•iSS1 

31-4 

.00285 

790 

.1283 

95° 

.1639 

31.6 

.00287 

8OO 

.1299 

IOOO 

•1723 

e  height  of  the  barometer  is  affected  by  the  relative  thermal  expansion  of  the  mercury  and 
3,  in  the  case  of  instruments  graduated  on  the  glass  tube,  and  by  the  relative  expansion  of 
:ury  and  the  metallic  inclosing  case,  usually  of  brass,  in  the  case  of  instruments  graduated 


*Thehei 
the  glass, 

the  mercury  and  the  metallic  inclosing  case,  usually  ( 
on  the  brass  case.  This  relative  expansion  is  practically  proportional  to  the  first  power  of  the  tem- 
perature. The  above  tables  of  values  of  the  coefficient  of  relative  expansion  will  be  found  to  give 
corrections  almost  identical  with  those  given  in  the  International  Meteorological  Tables.  The 
numbers  tabulated  under  a  are  the  values  of  a  in  the  equation  Ht  =  Hf  —  a  (/'—/)  where  ///  is  the 
height  at  the  standard  temperature,  Ht'  the  observed  height  at  the  temperature  /',  and  a  (t1  —  t)  the 
correction  for  temperature.  The  standard  temperature  is  o°  C.  for  the  metric  system  and  28°.  5  F. 
for  the  English  system.  The  English  barometer  is  correct  for  the  temperature  of  melting  ice  at  a 
temperature  of  approximately  28°.5  F.,  because  of  the  fact  that  the  brass  scale  is  graduated  so  as 
to  be  standard  at  62°  F.,  while  mercury  has  the  standard  density  at  32°  F. 

EXAMPLE.— A  barometer  having  a  brass  scale  gave  H '=  765  mm.  at  25°  C. ;  required,  the  cor- 
responding reading  at  o°  C.  Here  the  value  of  a  is  the  mean  of  .1235  and  .1251,  or  .1243  ;  .  • .  a(tf  —  t) 
=  .I243X  25  =  3.11.  Hence  ^0  =  765  —  3.11  =  761.89. 

N.  B. — Although  a  is  here  given  to  three  and  sometimes  to  four  significant  figures,  it  is  seldom 
worth  while  to  use  more  than  the  nearest  two-fiernre  number.  In  fact,  all  barometers  have  not  the 
same  values  for  a,  and  when  great  accuracy  is  wanted  the  proper  coefficients  have  to  be  deter- 
mined by  experiment. 

SMITHSONIAN  TABLES. 

1 2O 


TABLE  134. 


CORRECTION    OF    BAROMETER    TO   STANDARD   GRAVITY. 


Height 

Observed  height  of  barometer  in  millimetres. 

above  sea 

level  in 

metres. 

400 

450 

500 

550 

600 

650 

700 

750 

800 

100 

.014 

.015 

.016 

200 

.028 

.030 

.032 

300 

Correction   in   millime- 

.041 

.044 

.047 

4OO 

tres  for  elevation   above 

•055 

.059 

.063 

500 
600 
700 

sea  level  in   first  column 
and  height  of  barometer 
in  top  line. 

.064 
.077 
.090 

.o6§ 
.082 
.096 

.IO2 

.078 

800 

.103 

.109 

.117 

9OO 

.115 

.123 

•IS' 

IOOO 

.108 

.118 

.128 

•137 

.146 

1  100 

.118 

.130 

.141 

.150 

I2OO 

.129 

.142 

•154 

.164 

1300 

.140 

•153 

.166 

.178 

I4OO 

•151 

'!  6 

.179 

.191 

1500 

.147 

.162 

.191 

.205 

1600 

.1  57 

.172 

.188 

.204 

I7OO 

.167 

•183 

.200 

.217 

I800 
1900 
2000 
2IOO 
22OO 
2300 
2400 

.176 
.185 
.194 
.203 
.212 

.177 
.187 
.196 
.206 
.216 
.226 
.236 

.194 

.204 

•237 
.248 

•259 

.212 

.224 

•235 
.247 

•259 

.271 
.283 

.230 
.242 

•255 

1-345 
1.291 

•340 
.292 

•244 
.I96 
.149 

.245 
.203 
.162 
.I2O 
.088 
.046 
.004 

15000 
14500 
14000 
13500 
13000 
12500 

12000 

25OO 

.195 

.220 

.245 

.270 

•295 

1.237 

.IOI 

.962 

1  1  5OO  t^ 

26OO 

•203 

.229 

•255 

I.^I  C 

i  .184 

I.O53 

.920 

I  IOOO 

2700 
2800 
29OO 

•211 
.219 
.227 

.238 
.247 
.256 

.265 

•275 
.285 

1.050 

i'.255 

I.lrf 

1.136 

1.130 
1.076 
i.  022 

I.OO5 

•957 
.909 

.879 
•837 

•795 

IO5OO 
IOOOO 

9500 

3OOO 

•235 

.265 

.294 

.984 

1.076 

.969 

.861 

•753 

9000 

3100 

•243 

•274 

.918 

i.  oi  6 

.915 

.813 

8500 

3200 

.251 

.283 

•853 

•957 

.861 

.765 

8000 

3300 

.259 

.292 

1.077 

.787 

•897 

.807 

7500 

3400 

.267 

.2OI 

1.005 

.721 

.837 

•753 

7000 

3500 
3600 

•275 
•283 

•309 

•934 
.862 

.655 
.789 

•777 
.718 

.700 

6500 
6000 

37oo 

.291 

•79° 

.724 

.658 

5500 

3800 

•299 

•779 

.718 

.658 

.598 

5000 

3900 

•3°7 

.701 

.646 

•592 

4500 

4000 

•3H 

.623 

•574 

.526 

4000 

•5°3 
.419 

•545 
.467 

•389 

•503 
•431 
•359 

.461 
•395 

Corrections   in   hundredths 
of  an  inch  for  elevation  above 
sea  level  in  last  column   and 

3500 

3000 
2500 

•359 

•335 

•3" 

.287 

height  of  barometer  in  bottom 

2OOO 

.269 

•251 

•233 

•215 

line. 

I5OO 

.192 

.179 

.167 

.155 

IOOO 

.096 

.090 

.084 

.078 

500 

32 

30 

28 

26 

24 

22 

20 

18 

16 

14 

Height 

above  sea 

Observed  height  of  barometer  in  inches. 

level  in 
feet. 

SMITHSONIAN  TABLES. 


121 


TABLE  135. 

REDUCTION    OF    BAROMETER    TO   STANDARD    GRAVITY.* 

Reduction  to  Latitude  45°.  —  English  Scale. 

N.  B.     From  latitude  o°  to  44°  the  correction  is  to  be  subtracted. 
From  latitude  90°  to  46°  the  correction  is  to  be  added. 


Latitude. 

Height  of  the  barometer  in  inches. 

*9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

0° 

90° 

0.051 

0.053 

0.056 

0.059 

O.o6  1 

0.064 

0.067 

0.069 

0.072 

0.074 

0.077 

0.080 

5 

85 

0.050 

0.052 

0.055 

0.058 

0.060 

0.063 

0.066 

0.068 

0.071 

0.073 

0.076 

0.079 

6 

84 

.049 

.052 

•°55 

•057 

.060 

.062 

.065 

.068 

.070 

•073 

.076 

.078 

7 

83 

.049 

.052 

•054 

•057 

•059 

.062 

.065 

.067 

.070 

.072 

•075 

.077 

8 

82 

.049 

.051 

•054 

.056 

•059 

.061 

.064 

.067 

.069 

.072 

.074 

.077 

9 

81 

.048 

.051 

•053 

.056 

.058 

.061 

•063 

.066 

.068 

.071 

•073 

.076 

10 

80 

0.048 

0.050 

0.053 

0.055 

0.058 

0.060 

0.063 

0.065 

0.068 

0.070 

0-073 

0-075 

ii 

79 

.047 

.049 

.052 

•054 

•057 

•059 

.062 

.064 

.067 

.069 

.072 

.074 

12 

78 

.046 

.049 

•051 

•054 

.056 

.058 

.061 

.063 

.066 

.068 

.071 

•073 

J3 

77 

•045 

.048 

.050 

•053 

•055 

•057 

.060 

.062 

.065 

.067 

.069 

.072 

M 

76 

•045 

.047 

.049 

.052 

•054 

.056 

•°59 

.06! 

.063 

.066 

.068 

.071 

15 

75 

0.044 

0.046 

0.048 

0.051 

0-053 

0.055 

0.058 

O.o6o 

0.062 

0.065 

0.067 

0.069 

16 

74 

•043 

•045 

.047 

.050 

.052 

•054 

.056 

•059 

.061 

.063 

.065 

.068 

17 

73 

.042 

.044 

.046 

.049 

.051 

•053 

•055 

•057 

.060 

.062 

.064 

.066 

18 

72 

.041 

•043 

•045 

.047 

.050 

.052 

•054 

.056 

.058 

.060 

.062 

.065 

19 

7i 

.040 

.042 

.044 

.046 

.048 

.050 

.052 

•055 

•057 

•059 

.O6l 

.063 

20 

70 

0.039 

0.041 

0.043 

0.045 

0.047 

0.049 

0.051 

0-053 

0.055 

0.057 

0.059 

0.06  1 

21 

69 

.038 

.040 

.042 

.044 

•045 

.047 

.049 

.051 

•053 

•055 

•057 

•°59 

22 

68 

.036 

.038 

.040 

.042 

.044 

.046 

.048 

.050 

.052 

•054 

.056 

•057 

23 

67 

•035 

•037 

•039 

.041 

.043 

.044 

.046 

.048 

.050 

.052 

•054 

•055 

24 

66 

•034 

.036 

•037 

•039 

.041 

•043 

•045 

.046 

.048 

.050 

.052 

•053 

25 

65 

0.033 

0.034 

0.036 

0.038 

0.039 

0.041 

0.043 

0.044 

0.046 

0.048 

0.050 

O.O5I 

26 

64 

.031 

•°33 

.034 

.036 

.038 

•039 

.041 

•043 

.044 

.046 

.048 

.049 

27 

63 

.030 

.031 

•033 

•034 

.036 

.038 

•039 

.041 

.042 

.044 

•045 

.047 

28 

62 

.028 

.030 

.031 

•°33 

•034 

.036 

•037 

•039 

.040 

.042 

•043 

•045 

29 

61 

.027 

.028 

.030 

.031 

.032 

•034 

•°35 

•037 

.038 

•039 

.041 

.042 

30 

60 

O.O25 

0.027 

O.O28 

0.029 

0.031 

0.032 

0.033 

0.035 

0.036 

0.037 

0.039 

0.040 

3i 

59 

.024 

.025 

.026 

.027 

.029 

.030 

.031 

.032 

.034 

•035 

.036 

•037 

32 

58 

.022 

.023 

.025 

.026 

.027 

.028 

.029 

.030 

.032 

•033 

.034 

•°35 

33 

5£ 

.O2I 

.022 

.023 

.024 

.025 

.026 

.027 

.028 

.029 

.030 

.031 

.032 

34 

56 

.OI9 

.O2O 

.O2I 

.022 

.023 

.024 

.025 

.026 

.027 

.028 

.029 

.030 

35 

55 

0.017 

0.018 

0.019 

O.O2O 

0.021 

O.O22 

0.023 

0.024 

0.025 

O.O25 

0.026 

0.027 

36 

54 

.Ol6 

.Ol6 

.017 

.018 

.019 

.O2O 

.O2I 

.O2I 

.022 

.023 

.024 

.025 

37 

53 

.014 

.015 

.015 

.016 

.017 

.018 

.018 

.019 

.O2O 

.021 

.O2I 

.022 

38 

52 

.OI2 

.013 

.014 

.014 

.015 

.015 

.Ol6 

.017 

.017 

.018 

.019 

.019 

39 

5i 

.Oil 

.Oil 

.OI2 

.012 

.013 

.013 

.014 

.014 

..015 

.015 

,0l6 

.017 

40 

50 

O.OO9 

O.OO9 

O.OIO 

O.OIO 

O.OII 

O.OII 

O.OI2 

O.OI2 

O.OI2 

O.OI3 

O.OI3 

0.014 

4i 

49 

.007 

.007 

.008 

.008 

.009 

.009 

.009 

.OIO 

.010 

.OIO 

.Oil 

.Oil 

42 

48 

.005 

.006 

.006 

.006 

.006 

.007 

.007 

.007 

.008 

.008 

.008 

.008 

43 

47 

.004 

.004 

.004 

.004 

.004 

.004 

•005 

.005 

.005 

.005 

.005 

.006 

44 

46 

.002 

.002 

.002 

.OO2 

.002 

.002 

.OO2 

.002 

.003 

.003 

.003 

.003 

SMITHSONIAN  TABLES. 


"  Smithsonian  Meteorological  Tables,"  p.  58. 
122 


TABLE  136. 
REDUCTION    OF   BAROMETER   TO  STANDARD   GRAVITY.* 

Reduction  to  Latitude  45°.  —Metric  Scale. 

N.  B.  —  From  latitude  o°  to  44°  the  correction  is  to  be  subtracted. 
From  latitude  90°  to  46°  the  correction  is  to  be  added. 


Latitude. 

Height  of  the  barometer  in  millimetres. 

520 

560 

600 

620 

640 

660 

680 

700 

720 

740 

760 

780 

mm. 

mm. 

inni. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

0° 

90° 

I.38 

1.49 

i.  60 

1.65 

1.70 

1.76 

I.8l 

1.86 

I.92 

1.97 

2.02 

2.08 

5 

85 

.36 

•47 

•57 

1-63 

1.68 

J-73 

I.8l 

.84 

1.89 

1.94 

1.99 

2.04 

6 

84 

•35 

.46 

.56 

1.61 

1.67 

.72 

.78 

.82 

1.87 

J-93 

I  98 

2.03 

7 

83 

•34 

•45 

•55 

.60 

1.65 

.70 

•77 

.81 

1.86 

.QI 

1.96 

2.01 

8 

82 

•33 

•43 

•54 

•59 

1.64 

.69 

.76 

•79 

1.84 

•oQ 

1.94 

2.OO 

9 

81 

•32 

.42 

•52 

•57 

1.62 

.67 

•74 

•77 

1.82 

.87 

I.92 

1-97 

10 

80 

•3° 

.40 

•5° 

•55 

1.  60 

•65 

.70 

•75 

.80 

•85 

1.90 

'•95 

ii 

79 

.28 

•38 

.48 

•53 

1.58 

•63 

.68 

•73 

•78 

•83 

1.88 

'•93 

12 

78 

.26 

•36 

.46 

•51 

1.56 

.60 

•65 

.70 

•75 

.80 

1.85 

1.90 

*3 

77 

.24 

•34 

•44 

.48 

r-53 

•58 

•63 

.67 

.72 

•77 

1.82 

1.87 

H 

76 

.22 

•32 

.41 

.46 

1.50 

•55 

.60 

.65 

.69 

•74 

1.79 

1.83 

15 

75 

.20 

.29 

•38 

i-43 

1.48 

•52 

•57 

.61 

.66 

•7i 

i-75 

i.  80 

16 

74 

•17 

.26 

•35 

1.40 

1.44 

•49 

•54 

•58 

•63 

.67 

1.72 

1.76 

17 

73 

•!5 

.24 

•32 

•37 

1.41 

•45 

.50 

•54 

•59 

•63 

1.68 

1.72 

18 

72 

.12 

.21 

.29 

•34 

1.38 

.42 

.46 

•5i 

•55 

•59 

1.64 

1.68 

!9 

7i 

.09 

•17 

.26 

•30 

i-34 

•38 

•43 

•47 

•5i 

•55 

i-59 

1.64 

20 

70 

.06 

.14 

.22 

.26 

i-3i 

•35 

•39 

43 

•47 

•5i 

i-55 

i-59 

21 

69 

•°3 

.11 

.19 

•23 

1.27 

•31 

•35 

•38 

.42 

.46 

1.50 

i-54 

22 

68 

.00 

.07 

•!5 

.19 

1.23 

.26 

•3° 

•34 

•38 

.42 

1.46 

1.49 

23 

67 

0.96 

.04 

.11 

•15 

1.18 

.22 

.26 

.29 

•33 

•37 

1.41 

1.44 

24 

66 

•93 

.OO 

1.07 

.10 

1.14 

.18 

.21 

•25 

.28 

•32 

i-35 

J-39 

25 

65 

0.89 

0.96 

1.03 

.06 

I.IO 

•33 

.16 

.20 

•23 

.27 

1.30 

i-33 

26 

64 

•85 

.92 

0.98 

.02 

1.05 

.08 

.11 

•15 

.18 

.21 

1.25 

1.28 

27 

63 

.81 

.88 

•94 

0.97 

I.OO 

•03 

.06 

.IO 

•13 

.16 

1.19 

1.22 

28 

62 

•77 

•83 

.89 

.92 

0-95 

0.98 

.01 

1.04 

1.07 

.IO 

1-13 

1.16 

29 

61 

•73 

•79 

.85 

.87 

.90 

•93 

0.96 

0.99 

i.  02 

.04 

1.07 

I.IO 

30 

60 

0.69 

0-75 

0.80 

0.83 

0.85 

0.88 

0.91 

0.94 

0.96 

0.98 

I.OI 

1.04 

31 

59 

.65 

.70 

•75 

•77 

.80 

.82 

•85 

•87 

.90 

•92 

°-95 

0.97 

32 

58 

.61 

•65 

.70 

.72 

•75 

•77 

•79 

.82 

.84 

.86 

.89 

.91 

33 

57 

•56 

.61 

•65 

.67 

.69 

•71 

•74 

.76 

.78 

.80 

.82 

.84 

34 

56 

•52 

.56 

.60 

.62 

.64 

.66 

.68 

.70 

.72 

•74 

.76 

.78 

35 

55 

0.47 

0.51 

o-55 

0.56 

0.58 

0.60 

0.62 

0.64 

0.66 

0.67 

0.69 

0.71 

36 

54 

•43 

.46 

•49 

•5i 

•53 

•54 

.56 

•58 

•59 

.61 

.63 

.64 

37 

53 

•38 

.41 

•44 

•45 

•47 

.48 

•5° 

•51 

•53 

•54 

•56 

•57 

38 

52 

•33 

-36 

•39 

.40 

.41 

•43 

.44 

•45 

.46 

.48 

•49 

.50 

39 

5i 

.29 

•3i 

•33 

•34 

•35 

•37 

•38 

•39 

.40 

.41 

.42 

•43 

40 

50 

0.24 

0.26 

0.28 

0.29 

0.30 

0.31 

0.31 

0.32 

o-33 

0-34 

o-3| 

0.36 

4i 

40 

.19 

.21 

.22 

•23 

.24 

.24 

•25 

.26 

.27 

.27 

.28 

.29 

42 

48 

.14 

.16 

•17 

•17 

.18 

.18 

.19 

.19 

.20 

.21 

.21 

.22 

43 

47 

.10 

.IO 

.11 

.12 

.12 

.12 

•!3 

•J3 

•!3 

.14 

.14 

.14 

44 

46 

•05 

•°5 

.06 

.06 

.06 

.06 

.06 

.07 

.07 

.07 

.07 

.07 

SMITHSONIAN  TABLES. 


*  "  Smithsonian  Meteorological  Tables,"  p.  59. 
123 


TABLE  137. 


CORRECTION  OF  THE   BAROMETER  FOR  CAPILLARITY.* 


i.   METRIC  MEASURE. 

HEIGHT  OF  MENISCUS  IN  MILLIMETRES. 

Diameter 
of  tube 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

in  mm. 

Correction  to  be  added  in  millimetres. 

4 

0.83 

1.22 

i-54 

1.98 

2-37 

_ 

_ 

•47 

0.65 

0.86 

i-45 

i.  80 

- 

_ 

6 

.27 

.41 

.56 

0.78 

0.98 

1.  21 

i-43 

_ 

7 

.18 

.28 

.40 

•53 

.67 

0.82 

0.97 

I-I3 

8 

- 

.20 

.29 

.46 

.56 

•65 

0.77 

9 

- 

•15 

.21 

.28 

•33 

.40 

.46 

•52 

10 

— 

— 

.15 

.20 

•25 

.29 

•33 

•37 

ii 

— 

— 

.10 

.14 

.18 

.21 

.24 

.27 

12 

- 

- 

.07 

.10 

•J3 

•15 

.18 

.19 

U 

.04 

.07 

.10 

.12 

•13 

.14 

2.  BRITISH  MEASURE. 

HEIGHT  OF  MENISCUS  IN  INCHES. 

Diameter 
of  tube 
in  inches. 

.01 

.02 

.03 

.04 

.05 

.06 

.07 

.08 

Correction  to  be  added  in  hundredths  of  an  inch. 

•15 

2.36 

4.70 

6.86 

9-23 

11.56 

_ 

_ 

_ 

.20 

•25 

1.  10 

2.20 
1.  2O 

3.28 
1.92 

4-54 
2.76 

5-94 
3-68 

7.85 
4.72 

5.88 

_ 

•30 

•3§ 

0.79 

1.26 

1.77 

2.30 

2.88 

348 

4.20 

•35 

— 

•51 

0.82 

IiI5 

1.49 

1.85 

2.24 

2.65 

.40 

— 

.40 

.61 

0.81 

1.02 

1.22 

1.42 

1.62 

•45 

- 

•32 

.51 

0.68 

0.83 

0.96 

I-I5 

•5° 

— 

— 

.20 

•35 

•47 

.56 

.64 

0.71 

•55 

.08 

.20 

•31 

.40 

•47 

•52 

*  The  first  table  is  from  Kohlrausch  (Experimental  Physics),  and  is  based  on  the  experiments  of  Mendelejeff  and 
Gutkowski  (Jour,  de  Phys.  Chem.  Geo.  Petersburg,  1877,  or  Wied.  Beib.  1867).  The  second  table  has  been  calcu- 
lated from  the  same  data  by  conversion  into  inches  and  graphic  interpolation. 

A  number  of  tables,  mostly  based  on  theoretical  formulas  and  the  capillary  constants  of  mercury  in  glass  tubes  in 
air  and  vacuum,  were  given  in  the  fourth  edition  of  Guyot's  Tables,  and  may  be  there  referred  to.  They  are  not 
repeated  here,  as  the  above  is  probably  more  accurate,  and  historical  matter  is  excluded  for  convenience  in  the  use 
of  the  book. 

SMITHSONIAN  TABLES. 

I24 


TABLE  138, 


ABSORPTION  OF  CASES  BY  LIQUIDS/ 


ABSORPTION  COEFFICIENTS,  at,  FOR  GASES  IN  WATER. 

Temperature 

Centigrade. 

t 

Carbon 
dioxide. 
C02 

Carbon 
monoxide. 
CO 

Hydrogen. 
H 

Nitrogen. 

Nitric 
oxide. 
NO 

Nitrous 
oxide. 
N2O 

Oxygen. 
0 

O 

1.797 

0-0354 

O.O2IIO 

0.02399 

0.0738 

I-305 

0.04925 

5 

1.450 

•°3  i  5 

.O2O22 

.02134 

.0646 

1.095 

•04335 

10 

I.l85 

.0282 

.01944 

.01918 

•0571 

0.920 

.03852 

15 

I.OO2 

.0254 

.01875 

.01742 

•0515 

0.778 

•03456 

20 

0.901 

.0232 

.01809 

.01599 

.0471 

0.670 

•03137 

25 

C.772 

.0214 

•01745 

.01481 

.0432 

— 

.02874 

3° 

.0200 

.01690 

.01370 

_ 

.02646 

40 

0.506 

.0177 

.01644 

.01195 

- 

- 

.02316 

5° 

— 

.0161 

.01608 

.01074 

— 

— 

.02080 

100 

0.244 

— 

.Ol6oO 

.01011 

— 

— 

.01690 

Temperature 
Centigrade. 

t 

Air. 

Ammonia. 
NH3 

Chlorine. 
Cl 

Ethylene. 
C2H4 

Methane. 
CH4 

Hydrogen 
sulphide. 
H2S 

Sulphur 
dioxide. 
S02 

O 

0.02471 

II74.6 

3-036 

0.2563 

0.05473 

4-371 

79-79 

5 

.02179 

971-5 

2.8o8 

•2153 

.04889 

3-965 

67.48 

10 

•01953 

840.2 

2-5L5 

•1837 

.04367 

3-586 

56.65 

15 

•01795 

7^6.0 

2.388 

.1615 

.03903 

3-233 

47.28 

20 

.01704 

683.1 

2.156 

.1488 

•03499 

2.905 

39-37 

25 

~ 

610.8 

1.950 

~ 

.02542 

2.604 

32-79 

ABSORPTION  COEFFICIENTS,  at,  FOR  GASES  IN  ALCOHOL,  C2H5OH. 

Centigrade. 
t 

Carbon 
dioxide. 
C02 

Ethylene. 
C2H4 

Methane.    Hydrogen. 
CH4              H 

Nitrogen. 

Nitric 
oxide. 
NO 

Nitrous 
oxide. 
N2O 

Hydrogen     Sulphur 
sulphide,     dioxide. 
H2S            SO, 

0 

5 

4.329 
3.891 

3-595 
3-323 

0.5226       0.0692 
.5086         .0685 

0.1263 
.1241 

0.3161 
.2998 

4.190 
3-838 

17.89        328.6 
14.78        251.7 

10 

3-SH 

3.086 

.4953         .0679 

.1228 

.2861 

3-525 

11.99        190.3 

*5 

3-J99 

2.882 

.4828         -0673 

.1214 

.2748 

3-215 

9-54       144-5 

20 

2.946 

2.7J3 

.4710         .0667 

.1204 

•2659 

3-01  5 

7.41       114.3 

25 

2.756 

2.578 

.4598          .0662 

.1196 

•2595 

2.819 

5.62        99.8 

*  This  table  contains  the  volumes  of  different  gases,  supposed  measured  at  o°  C.  and  76  centimetres'  pressure,  which 
unit  volume  of  the  liquid  named  will  absorb  at  atmospheric  pressure  and  the  temperature  stated  in  the  first  column. 
The  numbers  tabulated  are  commonly  called  the  absorption  coefficients  for  the  gases  in  water,  or  in  alcohol,  at  t!>e 
temperature  t  and  under  one  atmosphere  of  pressure.  The  table  has  been  compiled  from  data  published  by  Bohr  & 
Bock,  Bunsen,  Carius,  Dittmar,  Hamberg,  Henrick,  Pagliano  &  Emo,  Raoult,  Schonfeld,  Setschenow,  and  Winkler. 
The  numbers  are  in  many  cases  averages  from  several  of  these  authorities. 

XOTE. —  The  effect  of  increase  of  pressure  is  generally  to  increase  the  absorption  coefficient.     The  following  is 
approximately  the  magnitude  of  the  effect  in  the  case  of  ammonia  in  alcohol  at  a  temperature  of  23°  C. : 
(  P    =  45  cms.         50  cms.         55  cms.         60  cms.         65  cms. 
I  a,3  =  69  74  79  84  88 

According  to  Setschenow  the  effect  of  varying  the  pressure  from  45  to  85  centimetres  in  the  case  of  carbonic  acid  in 
water  is  very  small. 
SMITHSONIAN  TABLES. 

125 


TABLE  139. 


VAPOR    PRESSURES. 


The  vapor  pressures  here  tabulated  have  been  taken,  with  one  exception,  from  Regnault's  results. 
The  vapor  pressure  of  Pictet  s  fluid  is  given  on  his  own  authority.  The  pressures  are  in  centimetres  oi 
mercury. 


Tem- 
pera- 
ture 
Cent. 

Acetone. 
C3H60 

Benzol. 
C6H6 

Carbon 
bisul- 
phide. 

Carbon 
tetra- 
chloride. 
CC14 

Chloro- 
form. 
CHC13 

Ethyl 
alcohol. 
C2H60 

Ethyl 
ether. 
C4H100 

Ethyl 
bromide. 
C2H6Br 

Methyl 
alcohol. 
CH40 

Turpen- 
tine. 

—25° 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

4.41 

.41 

_ 

—  20 

- 

•58 

4-73 

.98 

- 

•33 

6.89 

5-92 

•63 

- 

—'5 

- 

.00 

6.16 

T-35 

- 

8-93 

7.8l 

•93 

- 

—  IO 

— 

1.29 

7-94 

1.85 

— 

•65 

11.47 

10.15 

T-35 

- 

—5 

- 

1.83 

10.13 

2.48 

- 

.91 

14.61 

13.06 

1.92 

- 

0 

- 

2-53 

12.79 

3-29 

_ 

1.27 

18.44 

16.56 

2.68 

.21 

5 

— 

3-42 

1  6.00 

4-32 

— 

1.76 

23.09 

20.72 

3-69 

_ 

10 

- 

4-52 

19.85 

5.60 

- 

2.42 

28.68 

25-74 

5.01 

.29 

15 

— 

5.89 

24.41 

7.17 

— 

3-3° 

35-36 

31.69 

6.71 

20 

17.96 

7.56 

29.80 

9.10 

16.05 

4-45 

43-28 

38.70 

8.87 

.44 

25 

22.63 

9-59 

36.11 

11-43 

2O.O2 

5-94 

52.59 

46.91 

1  1.  60 

_ 

3° 

28.10 

12.02 

43.46 

14.23 

24-75 

7.85 

63.48 

56.45 

15.00 

.69 

35 
40 

34.52 
42.01 

'4-93 
18.36 

5T-97 
61-75 

17-55 
21.48 

30-35 
36-93 

10.29 
13-37 

76.12 
90.70 

67.49 
80.19 

19.20 
24-35 

i.  08 

45 

50.75 

22.41 

72.95 

26.08 

44.60 

17.22 

107.42 

94-73 

30.61 

- 

50 

62.29 

27.14 

85-71 

3M4 

53-5° 

21.99 

126.48 

111.28 

38-17 

1.70 

55 

72.59 

32.64 

100.16 

37-63 

63-77 

27.86 

148.11 

130.03 

47.22 

60 

86.05 

39.01 

116.45 

44-74 

75-54 

35-02 

172.50 

151.19 

57-99 

2.65 

65 

101.43 

46.34 

134-75 

52.87 

88.97 

43-69 

199.89 

1/4-95 

70.73 

70 

118.94 

54-74 

62.11 

104.21 

54-n 

230.49 

201.51 

85.71 

4.06 

75 

138.76 

64-32 

177.99 

72.57 

121.42 

66-55 

264-54 

231.07 

103.21 

_ 

80 

85 
90 

161.10 
186.18 
214.17 

75-J9 
87.46 
101.27 

203.25 
231.17 
261.91 

84.33 
97-51 
112.23 

140.76 
162.41 
186.52 

81.29 
98.64 
118.93 

302.28 
343-95 

263.86 
300.06 
339-89 

123-85 
147.09 
174.17 

6.13 
9.06 

95 

245-28 

116.75 

296-63 

128.69 

213.28 

142.51 

440.18 

383-55 

205.17 

- 

100 

279.73 

134.01 

332.5I 

146.71 

242.85 

169.75 

495-33 

43I-23 

240.51 

13.11 

I05 

317.70 

153.18 

372.72 

166.72 

275.40 

201.04 

555-62 

483.12 

280.63 

no 

359-40 

174.14 

416.41 

188.74 

311.10 

236.76 

621.46 

539-40 

325.96 

1  8.60 

115 

405.00 

197.82 

463-74 

212.91 

35°-10 

277-34 

693-33 

600.24 

376.98 

- 

I2O 

454-69 

223.54 

514.88 

239-37 

392.57 

323-17 

771.92 

665.80 

434.18 

25.70 

125 

508.62 

251.71 

569.97 

268.24 

438.66 

374.69 

_ 

736.22 

498.05 

_ 

130 

566.97 

282.43 

629.16 

299.69 

488.51 

432-30 

- 

811.65 

569-!  3 

34-90 

135 

629.87 

3  1  5-85 

692.59 

333-86 

542-25 

496.42 

— 

892.19 

647.93 

140 

697.44 

352-07 

760.40 

370.90 

600.02 

567.46 

— 

977.96 

733-71 

46.40 

J45 

- 

391.21 

832.69 

411.00 

661.92 

645.80 

- 

830.89 

150 

_ 

433-37 

909.59 

4  54-3  i 

728.06 

73^84 

_ 

_ 

936-13 

60.50 

155 

- 

478.65 

501.02 

798.53 

825.92 

- 

- 

68.60 

160 

- 

527-T4 

— 

551.31 

873.42 

- 

— 

- 

77-5° 

165 

- 

568.30 

- 

605.38 

952.78 

- 

- 

- 

- 

170 

634-07 

: 

663.44 

" 

i 

: 

" 

~ 

SMITHSONIAN  TABLES. 


126 


TABLE  139. 


VAPOR    PRESSURES. 


Tem- 
pera- 
ture, 
Centi- 
grade. 

Ammonia. 
NH3 

Carbon 
dioxide. 
C02 

Ethyl 
chloride. 
C2H5C1 

Ethyl 
iodide. 
C2H5I 

Methyl 
chloride. 
CH3C1 

Methylic 
ether. 
C2H60 

Nitrous 
oxide. 
N2O 

Pictet's 
fluid. 
64SOo+ 
44C02"by 
weight 

Sulphur 
dioxide. 
S02 

Hydrogen 
sulphide. 
H2S 

—30° 

86.61 

-    - 

1  1.  02 

- 

57-90 

57.65 

- 

58.52 

28.75 

- 

—25 

110.43 

1300.70 

14.50 

_ 

71.78 

71.61 

1569.49 

67.64 

37.38 

374.93 

—  20 

—  is 

139.21 
I73-65 

1514.24 
I758-25 

18.75 
23.96 

: 

88.32 
107.92 

88.20 

107.77 

1758.66 
1968.43 

74.48 
89.68 

47-95 
60.79 

443-85  1 

5J9-65 

—  10 

214.46 

2034.02 

30.21 

- 

130.96 

1  30.66 

2200.80 

101.84 

76.25 

608.46 

—5 

264.42 

2344-I3 

37-67 

— 

1  57-87 

I57-25 

2457.92 

121.60 

94.69 

706.60 

0 

318.33 

2690.66 

46.52 

4.19 

189.10 

187.90 

2742.10 

139.08 

116.51 

820.63 

5 
10 

383.03 
457-40 

3075-38 
3499-86 

56.93 
6r.ii 

5-41 
6.92 

225.11 
266.38 

222.90 
262.90  . 

3055-86 
3401.91 

167.20 

193.80 

142.11 
I?l-9S 

949.08 
1089.63 

15 

3964-69 

83.26 

8.76 

3I3-4i 

307.98 

3783-I7 

226.48 

206.49 

1244.79 

20 

638.78 

4471.66 

99.62 

II.OO 

366.69 

358.6o 

4202.79 

258.40 

246.20 

141  S^S 

25 

747.70 

5020.73 

118.42 

13.69 

426.74 

415.10 

4664.14 

297.92 

291.60 

1601.24 

3° 

870.10 

5611.90 

139.90 

16.91 

494.05 

477-So 

5*70-85 

338.20 

343-i8 

1803.53 

35 

1007.02 

6244.73 

164.32 

20.71 

569.11 

— 

6335.98 

383.80 

401.48 

2002.43 

40 

11  59-  53 

6918.44 

191.96 

25-17 

— 

434-72 

467.02 

2258.25 

45 

1328-73 

7631.46 

223.07 

30.38 

— 

- 

- 

478.80 

540-35 

2495-43 

50 

^s-Sa 

- 

257-94 

36.40 

- 

- 

- 

521-36 

622.00 

2781.48 

55 

1721.98 

— 

266.84 

43-32 

— 

— 

— 

— 

712.50 

3069.07 

60 

1948.21 

- 

340.05 

51.22 

- 

- 

- 

- 

812.38 

3374-02 

65 

2196.51 

- 

387-85 

- 

- 

- 

- 

922.14 

3696.15 

70 

2467.55 

— 

440.50 

— 

— 

— 

— 

— 

— 

4035-32 

75 

2763.00 

_ 

498.27 

- 

- 

- 

- 

- 

- 

- 

80 

3084.31 

- 

561.41 

- 

- 

- 

- 

- 

- 

- 

85 

3433-09 

— 

630.16 

— 

— 

— 

— 

— 

— 

— 

90 

3810.92 

- 

704.75 

- 

- 

- 

- 

- 

- 

- 

95 

4219.57 

— 

785-39 

— 

— 

~ 

— 

"• 

~ 

*" 

100 

4660.82 

- 

872.28 

- 

- 

- 

- 

- 

- 

— 

SMITHSONIAN  TABLES. 


127 


TABLES  14O-142. 

CAPILLARITY. -SURFACE    TENSION    OF    LIQUIDS.* 


TABLE  140.  — Water  and  Alcohol  in  Contact  with  Air. 


TABLE  142.  -  Solutions  of  Salts  in 
Water,  t 


Temp. 

Surface  tension 
in   dynes    per 
centimetre. 

Temp. 

Surface  tension 
in   dynes  per 
centimetre. 

Temp, 
c. 

Surface 
tension 
in  dynes 
per  cen- 
timetre. 

Salt  in 
solution. 

Density. 

Temp. 
C.° 

Tension 
in  dynes 
per  cm. 

Water. 

Ethyl 
alcohol. 

Water. 

Ethyl 
alcohol. 

BaCl2 

CaCl2 
a 

HC1 
« 
KC1 
« 
MgCla 
« 

NaCl 
a 

« 

NH4C1 
tt 

SrCl2 
K 
K2C03 

H 

Na2C03 

KNO3 

NaN03 

a 

CuS04 

H2SO4 
u 
K2SO4 

MgS04 
Mn2SO4 
ZnSO4 

N 

1.2820 
1.0497 

i-35" 

1-2773 

1.1190 

1.0887 

1.0242 

1.1699 

I.IOII 

1.0463 

1-2338 

1.1694 

1.0362 

1.1932 
1.1074 

1.0360 

1.0758 
1-0535 

1.0281 

1.3114 

1.1204 

1.0567 

1-3575 
1.1576 
1.0400 
1.1329 
1.0605 
1.0283 
1.1263 
i  .0466 
1.3022 
1.1311 

I-I775 
1.0276 
1.8278 

1-4453 
1.2636 
1.0744 
1.0360 
1.2744 
i.  0680 
1.1119 
1.0329 
1.3981 
1.2830 
1.1039 

15-16 
15-16 

*9 

19 

20 
20 

20 
15-161 

15-16 
15-16 
15-16 
15-16 
15-16 
20 

20 
2O 

16 

16 
16 
15-16 
15-16 
15-16 
15-16 
15-16 
15-16 
14-15 
14-15 
14-15 
14 
14 

12 
12 
15-16 
I5-l6 
15 
*5 

15-16 
15-16 
15-16 
15-16 
15-16 
15-16 
15-16 
15-16 
15-16 

8l.8 

77-5 
95-o 
90.2 

73-6 

74-5 

80.  i 
78.2 
90.1 
85.2 
78.0 
85.8 
80.5 
77-6 

84-3 
81.7 
78.8 
85.6 
79-4 
77-8 
00.9 
81.8 
77-5 
79-3 
77-8 
77.2 
78.9 
77-6 

83-5 
80.0 
78.6 
77.0 
63.0? 
79-7 
79-7 
78.0 

77-4 
83.2 

77-8 
79.1 

77-3 
833 
80.7 

77-8 

Water. 

0° 

5 
10 

i5 

20 

25 
30 
35 

75.6 

74-9 
74.2 

73-5 
72.8 
72.1 
71.4 
70.7 

23-5 
23.I 
22.6 
22.2 
21.7 
21.3 
20.8 

20.4 

40° 

45 
50 

II 

65 
70 

75 

70.0 

67^8 
67.I 
66.4 
65.7 
65.0 

20.0 

*9-5 
19.1 
18.6 
18.2 
17.8 

'7-3 
16.9 

80° 

85 

90 

95 

IOO 

64-3 
63-6 
62.9 
62.2 

61.5 

TABLE  141. 

-Miscellaneous  Liquids  in  Contact  with  Air. 

Liquid. 

Temp. 
C.° 

Surface 
tension 
in  dynes 
per  cen- 
timetre. 

Authority. 

Acel 
Acel 
Am} 
Ben; 
But) 
Cart 
Chk 
Etht 
Glyc 
Hex 
« 

Mer 
Met! 
Oliv 
Petr 

Prop 
u 

Tolu 
Turj 

on     .... 
ic  acid  .     .     . 
rl  alcohol    .     . 
:ene  .... 
rric  acid      .     . 
>on  disulphide 
>roform  .     .     . 

T          . 

14-0 
17.0 
15.0 
I5.0 
15.0 
20.0 
2O.O 
20.0 
17.0 

o.o 
68.0 

2O.O 
I5.0 
2O.O 
2O.O 

5-8 
97.1 
15.0 
109.8 

21.0 

25.6 
30.2 
24.8 
28.8 
28.7 

30-5 
28.3 
18.4 
63.14 
21.2 
14.2 
470.0 
24.7 

34-7 
25-9 
23.9 
•18.0 
29.1 
18.9 
28.5 

Average  of  various. 

« 
« 

a 

Quincke. 

Average  of  various. 
ft 

Hall. 
Schiff. 

Average  of  various. 

« 

Magie. 
Schiff. 

« 
Average  of  various. 

erine     .     .     . 
ane    .     .     .     . 

cury  .... 
ivl  alcohol 
e  oil  .     .     .     . 
oleum    . 
>yl  alcohol  .     . 

ol     .     .     ."     ! 
>entine  .     .     . 

*  This  determination  of  the  capillary  constants  of  liquids  has  been  the  subject  of  many  careful  experiments,  but  the 
results  of  the  different  experimenters,  and  even  of  the  same  observer  when  the  method  of  measurement  is  changed, 
do  not  agree  well  together.  The  values  here  quoted  can  only  be  taken  as  approximations  to  the  actual  values  for  the 
liquids  in  a  state  of  purity  in  contact  with  pure  air.  In  the  case  of  water  the  values  given  by  Lord  Rayleigh  from  the 
wave  length  of  ripples  (Phil.  Mag.  1890)  and  by  Hall  from  direct  measurement  of  the  tension  of  a  flat  film  (Phil.  Mag. 
1893)  have  been  preferred,  and  the  temperature  correction  has  been  taken  as  0.141  dyne  per  degree  centigrade.  The 
values  for  alcohol  were  derived  from  the  experiments  of  Hall  above  referred  to  and  the  experiments  on  the  effect  of 
temperature  made  by  Timberg  (Wied.  Ann.  vol.  30). 

The  authority  for  a  few  of  the  other  values  given  is  quoted,  but  they  are  for  the  most  part  average  values  derived 
from  a  large  number  of  results  published  by  different  experimenters. 

t  From  Volkmann  (Wied.  Ann.  vol.  17,  p.  353). 


SMITHSONIAN  TABLES. 


128 


TENSION    OF    LIQUIDS. 

TABLE  143. —Surface  Tension  of  Liquids.* 


TABLES  143-145, 


Liquid. 

Specific 
gravity. 

Surface  tension  in  dynes  per  cen- 
timetre of  liquid  in  contact  with  — 

Air. 

Water. 

Mercury. 

Water    

1.0 

'3-543 
1.2687 
1.4878 
0.7906 
0.9136 
0.8867 
9-7977 
1.  1C 

1.1248 

75-0 

s*y> 

<33°'i) 
(24.1) 

& 

297 

(729) 
69.9 

O.O 
392.0 
41.7 
26.8 

1  8.6 
"•5 

(28.9) 

(392) 

(387) 
(415) 
364 
317 
241 
271 

(392) 
429 

Bisulphide  of  carbon     

Ethyl  alcohol         
Olive  oil         _.'"'. 

Hyposulphite  of  soda  solution      .... 

TABLE  144.  —Surface  Tension  of  Liquids  at  Solidifying  Point. t 


Tempera- 

Surface 

Tempera- 

Surface 

Substance. 

solidifi- 

tension  in 
dynes  per 

Substance. 

solidifi- 

tension  in 
dynes  per 

Cent.° 

centimetre. 

Cent.0 

centimetre. 

Platinum 

2000 

1691 

Antimony 

432 

249 

Gold      .... 

I2OO 

IOO3 

Borax    .... 

IOOO 

216 

Zinc       .... 

360 

877 

Carbonate  of  soda 

IOOO 

2IO 

Tin         .... 

230 

Chloride  of  sodium 

— 

116 

Mercury 

—40 

588 

Water    .... 

o 

87.01 

Lead      .        V.      -. 

33° 

457 

Selenium 

217 

71.8 

Silver    .    ,     "«        .        . 

IOOO 

427 

Sulphur 

III 

42.1 

Bismuth 
Potassium 

265 
58 

1390 

Phosphorus  . 
Wax      .... 

23 

42.0 
34-i 

Sodium         ; 

90 

258. 

TABLE  145.  —  Tension  of  Soap  Films. 


Elaborate  measurements  of  the  thickness  of  soap  films  have  been  made  by  Reinolcl  and 
Rucker.y  They  find  that  a  film  of  oleate  of  soda  solution  containing  i  of  soap  to  70  of 
water,  and  having  3  per  cent  of  KNOs  added  to  increase  electrical  conductivity,  breaks  at 
a  thickness  varying  between  7.2  and  14.5  micro-millimetres,  the  average  being  12.1  micro- 
millimetres.  The  film  becomes  black  and  apparently  of  nearly  uniform  thickness  round 
the  point  where  fracture  begins.  Outside  the  black  patch  there  is  the  usual  display  of 
colors,  and  the  thickness  at  these  parts  may  be  estimated  from  the  colors  of  thin  plates 
and  the  refractive  index  of  the  solution  (vide  Newton's  rings,  Table  146). 

When  the  percentage  of  KNOg  is  diminished,  the  thickness  of  the  black  patch  increases. 
For  example,  KNO3  =3  i  0.5  o.o 

Thickness  =  12.4  13.5  14.5  22.1  micro-mm. 

A  similar  variation  was  found  in  the  other  soaps. 

It  was  also  found  that  diminishing  the  proportion  of  soap  in  the  solution,  there  being 
no  KNOs  dissolved,  increased  the  thickness  of  the  film. 

i  part  soap  to  30  of  water  gave  thickness  21.6  micro-mm. 

i  part  soap  to  40  of  water  gave  thickness  22.1  micro-mm. 

i  part  soap  to  60  of  water  gave  thickness  27.7  micro-mm.  • 

i  part  soap  to  80  of  water  gave  thickness  29.3  micro-mm. 


is  table  of  tensions  at  the  surface  separating  the  liquid  named  in  the  first  column  and  air,  water  or  mercury 
at  the  head  of  the  last  three  columns,  is  from  Quincke's  experiments  (Pogg.  Ann.  vol.  139,  and  Phil.  Mag. 


*  This 
as  stated 

1871).  The  numbers  given  are  the  equivalent  in  degrees  per  centimetre  of  those  obtained  by  Worthington  from 
Quincke's  results  (Phil.  Mag.  vol.  20,  1885)  with  the  exception  of  those  in  brackets,  which  were  not  corrected  by 
Worthington  ;  they  are  probably  somewhat  too  high,  for  the  reason  stated  by  Worthington.  The  temperature  was 
about  20°  C. 

t  Quincke,  "  Pogg.  Ann."  vol.  135,  p.  661. 

t  It  will  be  observed  that  the  value  here  given  on  the  authority  of  Quincke  is  much  higher  than  his  subsequent 
measurements,  as  quoted  above,  give. 

fl  "  Proc.  Roy.  Soc."  1877,  and  "  Phil.  Trans.  Roy.  Soc."  1881,  1883,  and  1893. 

NOTE.  —  Quincke  points  out  that  substances  may  be  divided  into  groups  in  each  of  which  the  ratio  of  the  surface 
tension  to  the  density  is  nearly  constant.  Thus,  if  this  ratio  for  mercurv  be  taken  as  unit,  the  ratio  for  the  bromides 
and  iodides  is  about  a  half  :  that  of  the  nitrates,  chlorides,  sugars,  and  fats,  as  well  as  the  metals,  lead,  bismuth,  and 
antimony,  about  i  ;  that  of  water,  the  carbonates,  sulphates,  and  probably  phosphates,  and  the  metals  platinum,  gold, 
silver,  cadmium,  tin,  and  copper,  2  ;  that  of  zinc,  iron,  and  palladium,  3  ;  and  that  of  sodium,  6. 


SMITHSONIAN  TABLES. 


I2Q 


TABLE  146. 


NEWTON'S   RINGS, 

Newton's  Table  of  Colors. 


The  following  table  gives  the  thickness  in  millionths  of  an  inch,  according  to  Newton,  of  a  plate  of  air,  water,  and 
glass  corresponding  to  the  different  colors  in  successive  rings  commonly  called  colors  of  the  first,  second,  third, 
etc.,  orders. 


Color  for  re- 
flected light. 

Color  for 
transmitted 
light. 

Thickness  in 

Color  for  re- 
flected light. 

Thickness  in 

millionths  of  an 

millionths  of  an 

1 

o 

inch  for  — 

13 

6 

Color 
for  trans- 
mitted 
light. 

inch  for  — 

1 

i 

i 

V, 

8 

re 

rt 

< 

Jj 

O 

< 

£ 

O 

I. 

Very  black 

_ 

0.5 

0.4 

O.2 

Yellow  .     . 

Bluish 

Black    . 

White  .     . 

1.0 

0.75 

0.9 

green 

27.1 

20.3 

T7-5 

Beginning 

Red  . 

. 

— 

29.0 

21.7 

18.7 

of  black 

. 

— 

2.O 

I.c 

1.3 

Bluish 

red 

— 

32.0 

24.0 

20.7 

Blue      . 

t 

Yellowish 

red  .     . 

2-4 

1.8 

I   r 

IV. 

Bluish 

White  . 

, 

Black  .     . 

S-2 

3-9 

3-4 

green    . 

— 

24.0 

25-5 

22.O 

Yellow  . 

Violet      . 

7.1 

5-3 

4.6 

Green 

Red    . 

35-3 

26.5 

22-7 

Orange 

. 

— 

8.0 

6.0 

4.2 

Yellowish 

Red  .     . 

. 

Blue    .    . 

9.0 

6.7 

5.8 

green     . 

— 

36.0 

27.0 

23.2 

Red. 

. 

Bluish 

II. 

Violet  . 

White      . 

II.  2 

3-4 

7-2 

green 

40-3 

30.2 

26.O 

Indigo  . 

. 

— 

12.8 

9.6 

8.4 

Blue      . 

Yellow     . 

14.0 

10.5 

9.0 

V. 

Greenish 

Green   . 

Red     .     . 

I5-1 

"•3 

9-7 

blue 

. 

Red   . 

46.0 

34-5 

39-7 

Yellow  . 

Violet      . 

16.3 

12.2 

10.4 

Red. 

. 

— 

52-5 

39-4 

34-o 

Orange 

— 

17-2 

13.0 

"•3 

Bright  red 

Blue    .     . 

18.2 

13-7 

1  1.8 

VI. 

Greenish 

Scarlet  . 

— 

19.7 

147 

12.7 

blue 

. 

— 

58.7 

46 

38.0 

Red. 

. 

— 

65.0 

48.7 

42.0 

III. 

Purple  . 
Indigo  . 

Green 

2I.O 
21.  1 

'5-7 
17.6 

'3-5 
14.2 

VII. 

Greenish 

Blue      . 

Yellow    . 

23.2 

blue  .     . 

— 

72.0 

53-2 

45-8 

Green   . 

Red     .     . 

25.2 

18.6 

16.2 

Reddish 

white 

— 

71.0 

57-7 

49.4 

The  above  table  has  been  several  times  revised  both  as  to  the  colors  and  the  numerical 

values.     Professors  Reinold  and  Rucker,  in  their  investigations  on  the  measurement  of  the 

thickness  of  soap  films,  found  it  necessary  to  make  new  determinations.   They  give  a  shorter 
series  of  colors,  as  they  found  difficulty  in  distinguishing  slight  differences  of  shade,  but 
divide  each  color  into  ten  parts  and  tabulate  the  variation  of  thickness  in  terms  of  the  tenth 
of  a  color  band.     The  position  in  the  band  at  which  the  thickness  is  given  and  the  order  of 

color  are  indicated  by  numerical  subscripts.    For  example  :  RI  5  indicates  the  red  of  the  first 
order  and  the  fifth  tenth  from  the  edge  furthest  from  the  red  edge  of  the  spectrum.     The 

thicknesses  are  in  millionths  of  a  centimetre. 

| 

Color. 

Posi- 

Thick- 

fc 

Color. 

Posi- 

Thick- 

& 

Color. 

Posi- 

Thick- 

E 

tion. 

ness. 

"S 

tion. 

ness. 

U 

tion. 

ness. 

° 

o 

o 

I. 

Red*    . 

R!  5 

28.4 

Red*    . 

R35 

76.5 

VI. 

Green    . 

G60 

141.0 

Bluish 

Green* 

G65 

147.9 

II. 

Violet    . 

V25 

3°-5 

red*  . 

BR35 

8l.5 

Red  .     . 

Reo 

154.8 

Blue  .     . 

B2  5 

35-3 

Red*     . 

Res 

162.7 

Green    . 

G2  5 

40.9 

IV. 

Green    . 

G4  o 

84.1 

Yellow  * 

Y25 

45-4 

" 

G45 

89-3 

VII. 

Green    . 

GV  0 

170.5 

Orange  * 

025 

49.1 

Yellow 

Green*. 

G75 

178.7 

Red  .     . 

R2  6 

52.2 

green  *    " 

^G4  5 

96.4 

Red  .     . 

RTO 

186.9 

Red*    . 

R4  5 

105.2 

Red*    . 

RT  5 

193.6 

III. 

Purple  . 

P35 

55-9 

Blue  .     . 

f^8  0 

57-7 

V. 

Green    . 

GS  o 

III.Q 

VIII. 

Green    . 

Gg  o 

200-4 

Blue*    . 

B35 

60.3 

Green  *  . 

GS  5 

II8.8 

Red  .     . 

RS  o 

211.5 

Green    . 

G36 

65.6 

Red  .     . 

Rso 

126.0 

Yellow  * 

Y.5 

71.0 

Red*     . 

R55 

133-5 

*  The  colors  marked  are  the  same  as  the  corresponding  colors  in  Newton's  table. 
SMITHSONIAN  TABLES. 

130 


CONTRACTION    PRODUCED    BY    SOLUTION.* 


TABLE  147, 


Across  the  top  of  the  heading  are  given  the  formulas  of  the  salt  dissolved,  its  molecular  weight  (M.  W. ),  and  the  den- 
sity of  the  salt,  with  the  authority  for  that  density. 


Grammes  of 
the  salt  in 
TOO  of  water. 

Observed 
volume. 

Calculated 
volume. 

Per  cent 
of 
contraction. 

Grammes  of 
the  salt  in 
100  of  water. 

Observed 
volume. 

Calculated 
volume. 

Per  cent 
of 
contraction. 

K2O. 

NaOH. 

M.  W.  =  47.02.    Density  =  2.656  (Karsten). 

M.  W.  =  39.95.    Density  =  2  .  1  30  (  Filhol  ). 

(Hager.) 

(Schiff.) 

4702 
9.404 
14.106 
18.808 
23.510 
28.212 

32-9l4 
37.616 
42.318 
47-020 
70.530 
79-934 

99.88 
99.92 
lOO.lS 
IOO.6o 
101.20 
102.00 
102.90 
103.90 
104.96 
106.10 
112.20 
114.88 

101.77 
103-55 
105-32 
107.09 
108.86 
110.64 
112.41 
114.18 
115.96 

"773 
126.59 
130.14 

1.86 
4.20 
4.88 
6.06 
7.04 
7.81 
8.46 
9.01 
9.80 
9.88 
"•37 
"•73 

3-995 
7.990 
11.985 
I5-980 

19-975 
23.970 
27.965 
31.960 
35-955 
39-95° 
59.925 
79.900 

99.4 

99.4 
99.6 
IOO.2 

100.8 
101.7 
102.7 
103.8 

105.0 

100.2 

II3-4 
121.  2 

101.88 
.     103.75 
105-63 
107.50 
109.38 
111.26 

"3-13 
115.01 
116.88 
118.76 
128.14 

I37«52 

2-43 
4.19 

5-71 

6.79 
7.84 

8-59 
9.22 

9-75 
10.17 
10.58 
11.50 
11.87 

119.850 

138.6 

156.28 

11.31 

1  59.800 

156.6 

I75-04 

10.34 

199.750 

174.8 

193.80 

9.80 

KOH. 

239.970 

193.6 

212.56 

8.92 

M.  W.  —  56.     Density  —  2.044  (Filhol). 

(Schiff.) 

5-6 

IOI.2 

102.74 

1.50 

II.  2 

1  6.8 

IO2.6 
IO4.O 

105.48 
108.22 

2-73 
3-90 

M.  W.  =  17.     Density  =r  0.616  (Andreef). 

22.4 
28.0 

105.4 
106.8 

IIO.2O 
113.70 

C.OI 

6.07 

(Carius.) 

33-6 

108.4 

116.44 

6.91 

39-2 

IIO.O 

II9.I8 

7-70 

1-7 

102.5 

102.76 

0.25 

44.8 

in.6 

121.92 

8.46 

3-4 

105.0 

105.52 

0.49 

5°-4 

113.2 

124.66 

9.19 

5-1 

107.4 

108.28 

0.8  1 

56.0 

115.0 

127.40 

9.72 

6.8 

109.8 

1  1  1  .04 

1.  12 

84.0 

124.2 

I4I.IO 

11.98 

8-5 

112.  2 

113.80 

I.4I 

1  1  2.0 

134.6 

154.80 

13-°S 

10.2 

II4.6 

116.56 

1.68 

168.0 

157-6 

182.20 

J3-50 

II-9 

II7.0 

119.32 

1-95 

224.O 

181.8 

209.60 

13.26 

I3.6 

II9-4 

122.08 

2.20 

15-3 

I2I.8 

124.84 

2.44 

17.0 

124.2 

127.60 

2.66 

25-5 

135-8 

141.40 

3-96 

Na2O. 

M  .  W.  =  30.97.     Density  =  2  .  805  (  Karsten). 

34-o 
51.0 

147-3 
169.7 

155.20 
182.80 

5-09 
7.17 

(Hager.) 

3-097 

99.01 

IOI.IO 

'      2.07 

6.194 
9.291 
12.388 

98.26 
97.76 

97-45 

IO2.2I 

103.31 
10442 

3.86 
1% 

NH4C1. 

M.  W.  r=  53.  38.     Density  —  i  .  52  (  Schroeder  ). 

I5-485 
18.582 

97-29 
97-23 

IO|-52 

106.63 

7.0O 

8.81 

(Gerlach.) 

21.679 

97-32 

107-73 

9.66 

24.776 

97-55 

108.83 

10.37 

5.338 

103.7 

103-51 

0.18 

27-873 

97.84 

109.94 

n.oo 

10.676 

107-5 

107.02 

0-45 

30.970 

98.20 

111.04 

11.56 

16.014 

III-5 

110.54 

0.87 

46.455 
52.649 

100.94 
102.30 

116.56 
118.77 

13.40 
13-87 

21-352 
26.690 

"  5-3 
119.2 

114.05 
117.56 

I.IO 

1.40 

*  The  table  was  compiled  from  a  paper  by  Gerlach  (Zeits.  fur  Anal.  Chem.  vol.  27). 
SMITHSONIAN  TABLES. 


TABLE  147. 


CONTRACTION    PRODUCED    BY   SOLUTION. 


Grammes  of 
the  salt  in 
100  of  water. 

Observed 
volume. 

Calculated 
volume. 

Per  cent 
of 
contraction. 

Grammes  of 
the  salt  in 
ico  of  water. 

Observed 
volume. 

Calculated 
volume. 

Per  cent 
of 
contraction. 

KC1. 
M.  W.  =  74.41.     Density  =  1.945  (Clarke). 

BaCl2. 
M.  W.  =r  207.  54.     Density  =3.75  (Schroeder). 

(Gerlach.) 

(Gerlach.) 

7.441 
14.882 
22.323 

102.8 
105.8 
108.9 

103-83 
107.65 
111.48 

0.99 
1.72 
2.3I 

IO-377 
20.754 

3i-!3i 

101.6 
102.9 
104.9 

102.77 

103.53 

108.30 

I.I4 

2.50 
3-14 

NaCl. 
M.  W.  —  58.36.     Density  =  2.150  (Clarke). 

KI. 

M.  W.  =  166.57.     Density  =  3.07  (Clarke). 

(Gerlach.) 

(Kremers. 

5.836 
11.672 
17.508 

23-344 
29.180 

IOI-7 

103-7 
105.8 
107.9 
IIO.I 

102.71 

105.43 
108.14 

110.86 
113.58 

0.99 
1.64 
2.16 
2.67 
3-06 

16.657 

33-3*4 

49.971 
66.628 
83.285 

104.5 
109.3 
114.2 
119.1 
124.0 

I05-39 
110.77 
116.18 
121.57 
126.97 

0.85 

i-34 
1.70 

2.  2O 

2-34 

M.  W. 

LiCl. 

lach). 

KClOg. 

M.  W.  =  122.29.     Density  =  2.331  (Clarke). 

42.                y      i  9     (.    e 

(Kremers.) 

(Gerlach.) 

6.114 

IO2-3 

102.62 

0.314 

4.2 
8.4 
12.6 

1  6.8 

2I.O 
42.O 

101.9 

103.8 
105.8 
107.8 
IIO.O 
I2O-7 

102.14 
104.28 
106.42 
108.56 
1  10.70 
121.40 

0.24 
0.46 
0.58 
0.70 
0.63 
0.58 

KN03. 
M.  W.  =  100.93.     Density  =  2.092  (Clarke). 

(Gerlach.) 

CaCl2. 

M.  W.  =  110.64.     Densi  y  =  2.216  (Schroeder). 

5.046 
10.093 
20.186 

101.90 
104.84 
108.40 

102.41 
104.83 
109.65 

0.50 

0.79 
1.14 

(Gerlach.) 

NaNO3. 
M.  W.  =  84.88.     Density  =  2.244  (Clarke). 

5-532 
11.064 
16.596 
22.128 
27.660 

33-192 
66.384 

IOI.2 
IO2.2 

T03-5 
104.8 
106.3 
I08.0 
II8.6 

102.50 
104.99 
107.49 
109.99 
112.48 
114.98 
129.96 

1.26 

2.66 

3-7i 
4.72 

5-50 
6.07 
8.74 

(Kremers.) 

8.488 
16.976 
42.440 
84.880 

102.9 
1  06.  1 

116.2 

J34-3 

103.78 
107.56 
118.91 
137.82 

0.85 
1.36 
2.28 

2-55 

RrCl,. 
M.  W.  —  1  57.94.     Density  =  3.05  (Schroeder). 

NH< 
79.90.     Dens 

N03. 

•oeder). 

(Gerlach.) 

(Gerlach.) 

7-895 
I5-790 
23.685 

SI'S** 

39-475 

101.4 
102.5 
104.0 

IOS-S 

107.2 

102.59 
105.17 
107.76 
110.34 
112.93 

1.16 

2-55 
3-43 
4-39 
5-°7 

7.990 
15.980 

39-95° 
79.900 

104.6 
109.3 
124.4 
149.8 

104.59 
109.18 
122.96 
145.92 

0.076 
O.I  06 
1.170 
2.660 

SMITHSONIAN  TABLES. 


132 


CONTRACTION    PRODUCED    BY   SOLUTION. 


TABLE  147. 


Grammes  of 
the  salt  in 
100  of  water. 

Observed 
volume. 

Calculated 
volume. 

Per  cent 
of 
contraction. 

Grammes  of 
the  salt  in 
100  of  water. 

Observed 
volume. 

Calculated 
volume. 

Per  cent 
of 
contraction. 

Ca(N08)2. 
M.  W.  =  163.68.     Density  =  2.36  (Clarke). 

NasCOg. 
M.  W.  =  105.83.  Density  2.476  (Clarke  and  Schroeder). 

(Gerlach.) 

(Gerlach.) 

I-637 
3-274 
4.910 

6-547 
8.184 
16.368 

32-736 
49.104 
65-472 
81.840 

100.45 
100.90 

IOI-35 
101.85 
102.30 
104.70 
109.90 

"5-55 
121.50 
127.65 

100.69 
101.39 
IO2.O8 
102.77 

10347 
106.94 
113.87 

120.81 

127.74 

134.68 

0.24 
0.48 
0.72 
0.90 

I-I3 
2.09 

3-49 

4-35 
4.89 
5-22 

5.292 
10.582 
I5-875 

100.00 
100.44 

101.06 

102.14 
104.27 
106.41 

5-°3 

K2S04. 
M.  W.  =  173.90.     Density  2.647  (Clarke). 

(Gerlach.) 

Ba(N03)2. 
M.  W.  =  260.58.     Density  =  3.23  (Clarke). 

8.695 

101.94 

103.29 

1.30 

(NH4)2S04. 
M.  W.  =  131.84.    Density  1.762  (Clarke). 

(Gerlach.) 

2.6o6 
5-212 
7.817 

100-5 
IOI.O 
IOI-5 

100.81 
101.61 
102.42 

0.30 
0.60 
0.90 

(Schiff.) 

6.592 
13.184 
19.776 
26.369 
65.920 
98.880 

102.92 
105.96 
109.20 
1  1  2.60 
135-20 
I54-50 

103.74 
107.48 
112.26 
114.97 
I37-42 
156.13 

0.792 
1.418 
I.82I 
2.060 
1.615 
1.044 

Sr(N03),. 
M.  W.  =r  2  10.98.    Density  =  2.93  (Clarke). 

(Gerlach.) 

FeS04. 
M.  W.  =  151.72.     Density  2.99  (Clarke). 

2.IIO 
4-220 
6.329 
8-439 
10.549 
21.098 
42.196 
63.294 

100.48 
100.95 
101.40 
I01.95 
102.45 
104.95 
IIO.2O 
II6.I5 

100.72 
101.44 
102.16 
102.88 
103.60 
107.20 
114.40 
121.60 

0.24 
0.48 
0.74 
0.90 
i.  ii 

2.10 

3-67 
4.48 

# 

7.586 
15.172 
22.758 
30-344 

100.52 
101.30 
102.40 
103.70 

102.54 
105.07 
107.61 
110.15 

1.97 

3-59 
4.84 
5.85 

Pb(N03)2. 
M.  W.  =  165.09.     Density  =  4.41  (Clarke). 

MgS04. 
M.  W.  =  197.6.    Density  2.65  (Clarke). 

(Gerlach.) 

16.509 
33.018 
82.545 

102.4 
105.1 
114.0 

103.74 
107.49 
118.72 

1.29 
2.22 

3-97 

• 

5.988 
11.976 
17.964 
23-952 

100.13 
100.40 
101.26 
102.10 

IO2.26 
104.52 
106.78 
109.04 

2.08 

3-94 
5.16 
6.36 

K,C03. 
1   M.  W.       137.93.    Density  2.29  (Clarke  and  Schroeder).  | 

(Gerlach.) 

Na,S04. 
M.  W.  —  141.80.     Density  =  2.656  (Clarke). 

6.897 

13-793 
20.689 
27.586 
68.965 
96.551 

100.96 
IO2.22 
103.78 
105.44 

118.20 
128.10 

103.01 
106.02 
109.08 
112.05 
130.12 
142.16 

1.99 

3-59 
4.82 

5-90 
9.16 
9.89 

(Gerlach.) 

7.09 
14.18 

100.96 
IO2.26 

102.67 
105.34 

1.67 
2.92 

SMITHSONIAN  TABLES. 


*  Authority  not  given. 


133 


TABLE   147. 


CONTRACTION    PRODUCED    BY   SOLUTION. 


Grammes  of 
the  salt  in 
100  of  water. 

Observed 
volume. 

Calculated 
volume. 

Per  cent 
of 
contraction. 

Grammes  of 
the  salt  in 
100  of  water. 

Observed 
volume. 

Calculated 
volume. 

Per  cent 
of 
contraction. 

ZnSO4. 
M.  W.  =  160.72.    Density  3.49  (Clarke). 

KC2H302. 
M.  W.  =  97.90.    Density  =  1.472  (Gerlach). 

# 

(Gerlach.) 

8.036 
16.072 
24.108     - 
32.144 
40.180 

IOO.O6 
100.44 
IOI.CJ8 
101.90 
102.86 

102.30 
104.61 
106.91 
109.21 
111.51 

i 

m 

7.76 

9-79 

19.58 

48.95 
97.90 

105.2 
IIO-5 

127-3 
156.4 

106.65 

II3.30 
Ig.26 
166.51 

I.36 
2-47 
4-47 
6.07 

K2C4H406. 

M.  W.  =  225.72.     Density  1.98  (Gerlach). 

A12K2(S04)4. 
M.  W.  =  128.99.    Density  =  2.228  (Clarke). 

(Gerlach.) 

(Gerlach.) 

6.450 

100.58 

102.90 

2.25 

22.572 

45-H4 
67.716 
90.288 
112.860 

I35-432 
1  58.004 

1  08.8 
118.3 
128.2 

138.7 
149.2 

IS9-7 

170.6 

111-39 
122.79 
134.18 
I45-58 
156.97 
168.36 
179.76 

446 
4-73 
4-95 
$-l$ 
5.10 

NaC2H802. 

M.  W.  =  81.85.    Density  =  1.476  (Gerlach). 

(Gerlach.) 

8.185 
16.360 

104.1 
108.3 

I05-55 
111.09 

J-37 
2.51 

Pb(C2H302)2. 
M.  W.  —  162.06.    Density  3.251  (Schroeder). 

Na2Q 

H406. 
snsity  1.83  (Gerlach). 

(Gerlach.) 

(Gerlach.) 

16.206 
32.412 
81.030 

104.7 
109.5 
124.6 

104.98 
109.96 
124.91 

0.27 
0.42 
0.25 

19.362 

38.724 

106.6 
114.2 

110-57 
121.15 

3-59 

5-74 

TABLE  148. 

CONTRACTION    DUE   TO   DILUTION   OF   A   SOLUTION.! 

The  first  column  gives  the  name  of  the  salt  dissolved,  the  second  the  amount  of  the  salt  required  to  produce  saturation 
and  the  third  the  contraction  produced  by  mixing  with  an  equal  volume  of  water. 


Parts  of  an- 

Parts  of  an- 

Water  with  equal  volume 
of  saturated  solution  of 

hydrate  salt 
dissolved  by 

Contraction 
when  mixed. 

Water  with  equal  volume 
of  saturated  solution  of 

hydrate  salt 
dissolved  by 

Contraction 
when  mixed. 

following  salts. 

100  parts  of 

Per  cent. 

following  salts. 

100  parts  of 

Per  cent. 

H2O  at  10°  C. 

H2Oatio°C. 

KC1     . 

3*«97 

°-325 

NH4N03     . 

185.00 

0.772 

K2SO4 

10.10 

0.082 

CaCl2  . 

63.30 

I-I35 

KN03  . 

20.77 

0.144 

BaCl2  . 

33-3° 

0.235 

K2C03 

88.72 

2.682 

MgS04 

30-50 

0.677 

NaCl    . 

35-75 

0.490 

ZnS04. 

48.36 

0.835 

Na2SO4 

8.04 

0.107 

FeS04  . 

19.90 

0.327 

NaNO3 
Na2CO8 

84.30 
1  6.66 

o-975 
0.206 

A12K2(S04)4         . 
CuS04. 

4.99 
20.92 

0.033 

O.2IO 

NH4C1 

36.60 

0.273 

Pb(N03)2     . 

48.30 

0.228 

(NH4)2S04  .        . 

I 

1.302 

SMITHSONIAN  TABLES. 


*  Authority  not  given. 

t  R.  Broom,  "  Proc.  Roy.  Soc.  Edin."  vol.  13,  p.  172. 


134 


TABLE  149, 


FRICTION. 

The  following  table  of  coefficients  of  friction  f  and  its  reciprocal  i  If,  together  with  the  angle  of  friction  or  angle  of 
repose  <£,  is  quoted  from  Rankine's  "Applied  Mechanics.''  It  was  compiled  by  Rankine  from  the  results  of 
General  Morin  and  other  authorities,  and  is  sufficient  for  all  ordinary  purposes. 


Material. 

/ 

l// 

* 

Wood  on  wood,  dry       ...... 
"      "      "       soapy  
Metals  on  oak,  dry         .        .        .        ... 
"        "      "    wet        .        .        .        . 

•25--50 
.20 
.5o-.6o 
.24-.  26 
.20 

4.00-2.00 
5.00 
2.00-1.67 

4-I7-3-85 
5.00 

14.0-26.5 

»-s 

26.5-31.0 

I3-5-M-5 
n-5 

..     .      =>u«>-H.y 
"    elm,  dry         
Hemp  on  oak,  dry          
"        "      "     wet          .        . 
Leather  on  oak      
"         "    metals,  dry  
"        «        "       wet  

.20-.25 

-S3 

•33 

.27-38 

$ 

5.00-4.00 
1.89 
3.00 
3.70-2.86 
1.79 
2.78 

11.5-14.0 
28.0 
18.5 
15.0-19.5 
29-5 

2O.O 

"        "        "       greasy     
"        "        "        oily     .    . 

•23 
•15 

$ 

6.67—5.00 

8.<;-ii.<; 

"       "        "wet  sr 
Smooth  surfaces,  occasionally  greased  . 
"            "        continually  greased   . 
"            "        best  results        .... 
Steel  on  agate,  dry  *      
"      "      "       oiled*  

.07-.o8 

•°s 

.03-.036 

.20 

.107 

3-33 
14.3-12.50 

20.00 

33-3-27-6 
5.00 

Q.-JC 

16.5 
4.0-4.5 

3-° 
1.75-2.0 

y-s 

6.1 

7.^-1.47 

16.7—  "?c.o 

Wood  on  stone      
Masonry  and  brick  work,  dry        ... 
"          '•      "        "        damp  mortar 
"       on  dry  clay      
"         "  moist  clay  
Earth  on  earth       
"       "       "     dry  sand,  clay,  and  mixed  earth   . 
"       "       "      damp  clay     
"       "       "      wet  clay        .                 ... 
"       "       "      shingle  and  gravel 

About  .40 
.6o-.70 
•74 
•Si 
•33 
.25-1.00 

•38-75 

1.  00 

.81-1.  ii 

2.50 

1.67-1.43 

$ 

3.00 
4.00-1  .00 
2.63-1.33 

I.OO 

3-23 
1.23-0.9 

22.O 

33-o-35-o 
36-5 
27.0 
18.25 
14.0-45.0 
21.0-37.0 
45-o 
17.0 
39.0-48.0 

*  Quoted  from  a  paper  by  Jenkin  and  Ewing,  "  Phil.  Trans.  R.  S."  vol.  167.   In  this  paper  it  is  shown  that  in 
cases  where  "  static  friction  "  exceeds  "  kinetic  friction  "  there  is  a  gradual  increase  of  the  coefficient  of  friction  as  the 
speed  is  reduced  towards  zero. 
SMITHSONIAN  TABLES. 

135 


TABLE   15O. 


VISCOSITY. 


The  coefficient  of  viscosity  is  the  tangential  force  per  unit  area  of  one  face  of  a  plate  of  the 
fluid  which  is  required  to  keep  up  unit  distortion  between  the  faces.  Viscosity  is  thus  measured 
in  terms  of  the  temporary  rigidity  which  it  gives  to  the  fluid.  Solids  may  be  included  in  this- 
definition  when  only  that  part  of  the  rigidity  which  is  due  to  varying  distortion  is  considered. 
One  of  the  most  satisfactory  methods  of  measuring  the  viscosity  of  fluids  is  by  the  observation 
of  the  rate  of  flow  of  the  fluid  through  a  capillary  tube,  the  length  of  which  is  great  in  compari- 
son with  its  diameter.  Poiseuille  *  gave  the  following  formula  for  calculating  the  viscosity  coef- 

ficient in  this  case  :  ju,  =  ~&vj~>  w^ere  ^  *s  tne  pressure  height,  r  the  radius  of  the  tube,  s  the 

density  of  the  fluid,  v  the  quantity  flowing  per  unit  time,  and  /  the  length  of  the  capillary  part  of 
the  tube.  The  liquid  is  supposed  to  flow  from  an  upper  to  a  lower  reservoir  joined  by  the  tube, 
hence  h  and  /  are  different.  The  product  /is  is  the  pressure  under  which  the  flow  takes  place. 
Hagenbach  t  pointed  out  that  this  formula  is  in  error  if  the  velocity  of  flow  is  sensible,  and  sug- 
gested a  correction  which  was  used  in  the  calculation  of  his  results.  The  amount  to  be  sub- 


tracted  from  h,  according  to   Hagenbach,  is  -= 


Gartenmeister  \  points  out  an  error  in  this  to  whic 


,  where  g  is  the  acceleration  due  to  gravity.. 

his  attention  had  been  called  by  Finkener,, 

v* 


and  states  that  the  quantity  to  be  subtracted  from  //  should  be  simply  —  ;  and  this  formula  is. 

g 

used  in  the  reduction  of  his  observations.  Gartenmeister's  formula  is  the  most  accurate,  but  alf 
of  them  nearly  agree  if  the  tube  be  long  enough  to  make  the  rate  of  flow  very  small.  None  of  the^ 
formulae  take  into  account  irregularities  in  the  distortion  of  the  fluid  near  the  ends  of  the  tube, 
but  this  is  probably  negligible  in  all  cases  here  quoted  from,  although  it  probably  renders  the 
results  obtained  by  the  "  viscosimeter  "  commonly  used  for  testing  oils  useless  for  our  purpose. 
The  term  "  specific  viscosity  "  is  sometimes  used  in  the  headings  of  the  tables  ;  it  means  the 
ratio  of  the  viscosity  of  the  fluid  under  consideration  to  the  viscosity  of  water  at  a  specified 
temperature. 

TABLE  150.  —  Specific  Viscosity  of  Water  at  different  Temperatures  relative  to  Water  at  0°  C. 


Authorities. 



Absolute 

Temp. 

Mean 

value  in 

inC°. 

value. 

C.  G.  S. 

Poiseuille. 

Graham. 

Rellstab. 

Sprung. 

Wagner. 

Slotte. 

units. 

0 

IOO.O 

IOO.O 

IOO.O 

IOO.O 

IOO.O 

IOO.O 

IOO.O 

IOO.O 

O.OI78§ 

5 

85.2 

84.4 

84.8 

85-3 

84-9 

- 

- 

84.9 

0.0151 

10 

73-5 

73-6 

72.9 

73-5 

73-2 

— 

— 

73-3 

0.0131 

15 

20 

64-3 
56.7 

63-5 
56.0 

03.7 

56.0 

63.0 

55-5 

63-9 
56.2 

63-9 
56.2 

56.4 

63-7 
56.2 

O.OII3 
O.OIOO 

25 

30 

45-2 

49-5 
44-7 

50-5 

45-° 

48.7 
45-° 

50-5 
45-2 

44.6 

45-2 

49.9 

45-° 

0.0089 
0.0080 

35 

— 

40.2 

41.1 

40.0 

40.8 

40-3 

40.5 

0.0072 

40 

- 

36.8 

37-o 

37-2 

37-o 

36.7 

36-9 

36-9 

0.0066 

45 

— 

33-9 

33-9 

34-5 

34-o 

34-5 

34-2 

0.006  1 

50 

30.8 

3i-i 

Si-* 

31.2 

3i-3 

3i-7 

- 

31.2 

0.0056 

*  "Comptes  rendus,''  vol.  15,  1842.     "  Me"m.  Serv.  Etr."  1846. 

t  "Pogg.  Ann."  vol.  109,  1860. 

t  "Zeits.  fiir  Phys.  Chim.';  vol.  6,  1890. 

§  The  value  0.0178  is  taken  from  a  paper  by  Crookes  (Phil.  Trans.  R.  S.  L.  1886),  where  the  coefficient  is  given  as 
H  =  0.017  7931 P,  where  P— *  =  i  +  . 03367937"+  .0002209936  Tz,  where  T  is  the  temperature  of  the  water  in  degrees 
Centigrade.  The  numbers  in  the  table  were  calculated  not  from  the  formula  but  from  the  numbers  in  the  column 
headed  "  mean  value." 

SMITHSONIAN  TABLES. 


136 


TABLES  151-153. 
VISCOSITY. 

TABLE  151.  -  Solution  of  Alcohol  in  Water.* 

Coefficients  of  viscosity,  in  C.  G.  S.  units,  for  solution  of  alcohol  in  water. 


Temp. 

Percentage  by  weight  of  alcohol  in  the  mixture. 

o 

8.21 

16.60 

34-58 

43-99 

53.36 

75-75 

87.45 

99.72 

0° 

O.OlSl 

0.0287 

0-0453 

0.0732 

0.0707 

0.0632 

0.0407 

0.0294 

0.0180 

5 

.0152 

.0234 

•0351 

.0558 

•0552 

.0502 

•0344 

.0256 

.0163 

10 

.0131 

.0195 

.0281 

•0435 

.0438 

.0405 

.0292 

.0223 

.0148 

15 

.0114 

.0165 

.0230 

•0347 

•°353 

•0332 

.0250 

.0195 

.0134 

20 

.OIOI 

.0142 

.0193 

.0283 

.0286 

.0276 

.0215 

.0172 

.0122 

25 

O.OOQO 

0.0123 

0.0163 

0.0234 

O.O24I 

O.O232 

0.0187 

O.OI52 

O.OIIO 

30 

.008I 

.0108 

.0141 

.0196 

.O2O4 

.0198 

.0163 

•OI35 

.OIOO 

35 

.0073 

.0096 

.0122 

.0167 

.0174 

.0171 

.0144 

.0120 

.0092 

40 

.0067 

.0086 

.0108 

.0143 

.0150 

.0149 

.0127 

.0107 

.0084 

45 

.Oo6l 

.0077 

.0095 

.0125 

.0131 

.0130 

•0113 

.0097 

.0077 

50 

0.0056 

O.OO7O 

0.0085 

0.0109 

O.OII5 

o.oi  1  5 

O.OIO2 

0.0088 

0.0070 

55 

.0052 

.0063 

.0076 

.0096 

.OIO2 

.0102 

.0091 

.0086 

.0065 

60 

.0048 

.0058 

.0069 

.0086 

.0091 

.0092 

.0083 

.0073 

.0060 

The  following  tables  (152-153)  contain  the  results  of  a  number  of  experiments  in  the  viscosity  of  mineral  oils  derived 
from  petroleum  residues  and  used  for  lubricating  purposes,  t 


TABLE  152. -Mineral  Oils.* 


g 

C     . 

'£  c 

m'o 

bJO 
C  j 

§1 

Sp.  viscosity.     Water  at 

20°  C.  =  I. 

1 

E  a 
0  C. 

20°  C. 

50°  C. 

100°  C. 

•931 

243 

274 

_ 

11.30 

2.9 

.921 
.906 

216 
189 

246 
208 

- 

7-31 
3-45 

2.5 

.921 

163 

190 

_ 

27.80 

2.8 

.917 

132 

1  68 

- 

- 

2.6 

•904 

170 

207 

8.65 

2.65 

1-7 

.891 

151 

182 

4-77 

1.86 

.878 

108 

148 

2-94 

1.48 

.855 

42 

45 

1.65 

- 

•905 

165 

202 

_ 

3.10 

J-5 

.894 

139 

270 

7.60 

3.60 

'•3 

.866 

90 

224 

2.50 

1.50 

TABLE  153. -Mineral  Oils. 


Oil. 

1 

1 

11 

Viscosity  at  1  1 
19°  C.,  water 
ati9°C.=i.  || 

Cylinder  oil  .     . 
Machine  oil  .     . 

.917 
.914 

227 
213 

274 
260 

191 

IO2 

Wagon  oil     .     . 

.914 

148 

182 

80 

Naphtha  residue 

.911 
.910 

157 
134 

187 
162 

70 

55 

Oleo-naphtha     . 

.910 

219 

2S7 

121 

.904 

2OI 

242 

66 

"          " 

.894 

I84 

222 

26 

Oleonid     .     .     . 

.884 

185 

217 

28 

best 

quality 

.881 

1  88 

224 

20 

Olive  oil    ... 

.916 

_ 

_ 

22 

Whale  oil      .     . 

.879 

- 

- 

9 

• 

.875 

8 

*  This  table  was  calculated  from  the  table  of  fluidities  given  by  Noack  (Wied.  Ann.  vol.  27,  p.  217),  and  shows  a 
maximum  for  a  solution  containing  about  40  per  cent  of  alcohol.  A  similar  result  was  obtained  for  solutions  of  acetic 
acid.  .» 

t  Table  152  is  from  a  paper  by  Engler  in  Dingler's  "  Poly.  Jour."  vol.  268,  p.  76,  and  Table  153  is  from  a  paper  by 
Lamansky  in  the  same  journal,  vol.  248,  p.  29.  The  very  mixed  composition  or  these  oils  renders  the  viscosity  a  very 
uncertain  quantity,  neither  the  density  nor  the  flashing  point  being  a  good  guide  to  viscosity. 

J  The  different  groups  in  this  table  are  from  different  residues. 

SMITHSONIAN   TABLES. 


137 


TABLE    154. 

VISCOSITY. 

This  table  gives  some  miscellaneous  data  as  to  the  viscosity  of  liquids,  mostly  referring  to  oils  and  paraffins.    The 

viscosities  are  in  C.  G.  S.  units. 


Liquid. 

G.% 

Coefficient 
of 
viscosity. 

Temp. 
Cent.  ° 

Authority. 

Ammonia      ..... 

0.0  1  60 

II.9 

Poiseuille. 

u 

0.0149 

14-5 

« 

O.OIII 

2O.O 

Gartenmeister. 

Glycerine                                        ; 

42.20 

2.8 

Schottner. 

M 

25.18 

8.1 

u 

u 

1787 



1  J-"/ 
8.30 

20.3 

** 

A.  QA. 

26.; 

Glycerine  and  water    . 

94.46 

7-437 

•**«j 

"... 

80.31 

1.  02  1 

8-5 

"                    "... 

64.05 

O.222 

8.5 

"... 

49-79 

0.092 

8.5 

M 

Glycol 

O.O2I9 

O.O 

Arrhenius. 

0.0184 

—  20 

Koch. 

a 

O.OI7O 

O.O 

"               ..... 

0.0157 

2O.O 

" 

"               ..... 

O.OI22 

IOO.O 

«' 

" 

0.0102 

200.0 

H 

"               

0.0093 

3OO.O 

M 

0.1878 

2O.O 

Gartenmeister. 

Olive  oil        ..... 

0.0 

Reynolds. 

Paraffins  :  Decane 

0.0077 

22-3 

Bartolli  &  Stracciati. 

Dodecane   . 

0.0126 

23-3 

« 

Heptane 

O.OO45 

24.0 

<                   « 

Hexadecane 

0.0359 

22.2 

'                   «« 

Hexane        .        .        . 

0.0033 

23-7 

<                        u 

Nonane       .        «        . 

0.0062 

22-3 

«« 

Octane 

0.0053 

22.2 

« 

Pentane       .         .         . 

O.OO26 

21  O 

"                     " 

Pentadecane 

O.O28l 

22.O 

U                                      ft 

Tetradecane 

0.0213 

21.9 

U                                   (« 

Tridecane    . 

0.0155 

23-3 

<«                     «« 

Undecane    . 

00095 

22.7 

«                         «( 

Petroleum  (Caucasian)         .        . 

O.OI9O 

17-5 

Petroff. 

2C  T, 

O.O 

O.  E.  Meyer. 

u      « 

3^5 

I  O.O 

u    "      .     .     .     .     ! 

1-63 

2O.O 

M 

«    « 

O.Q6 

7O.O 

« 

w  ;7 

O 

*  Calculated  from  the  formula  /u,—  .017  —  .000066* -f- 0000002 1^2—  .00000000025^  (vide  Koch,  Wied.  Ann.  vol.  14. 
p.  i). 

t  Given  as  :=  3.2653*— 0123:r,  where  Tis  temperature  in  Centigrade  degrees. 

SMITHSONIAN  TABLES. 

138 


TABLE  155, 


VISCOSITY. 

This  table  gives  the  viscosity  of  a  number  of  liquids  together  with  their  temperature  variation.    The  headings  are 
temperatures  in  Centigrade  degrees,  and  the  numbers  under  them  the  coefficients  of  viscosity  in  C.  G.  S.  units.* 


Liquid. 

Temperatures  Centigrade. 

Authority. 

10° 

20° 

30° 

40° 

50° 

Acetone    

.0043 
.0068 
.0106 

.0039 
.006l 
.OO89 

.0036 
.0054 
.0077 

.0032 
.0049 
.0065 

.0028 
.0044 
.0058 

Pribram  &  Handl. 

Acetates:  Allyl      .     .     . 
Amyl     , 

T-*     i        t 

Ethyl     .     .     . 
Methyl  .     .     . 
Propyl  .     .     . 
Acids  :  t  Acetic      .     .     . 

.0051 
.0046 
.0066 
.0150 

.0044 
.OO4I 
.0059 
.OI26 

.0040 
.0036 
.0052 
.OIO9 

.0032 
.0044 
.0094 

.0032 
.0030 

.0039 
.0082 

« 

Butyric 

.0196 

.0163 

.0136 

.OIl8 

.0102 

Gartenmeister. 

Formic     .     .     . 

.0231 

.Ol84 

.0149 

.0125 

.0104 

" 

Propionic      .     . 

.0125 

.OI07 

.0092 

.008I 

.0073 

Rellstab. 

" 

.0139 

.0118 

.0101 

.0091 

.0080 

Pribram  &  Handl. 

Salicylic   .     .     . 

.0320 

.O27I 

.0222 

.Ol8l 

.0150 

Rellstab. 

Valeric     .     .     . 

.0271 

.O22O 

.0183 

•OI55 

.0127 

" 

Alcohols:  Allyl.     .     .     . 

.0206 

.Ol63 

.0128 

.0103 

.0083 

Pribram  &  Handl. 

Amyl     .     .     . 

.0651 

.0470 

•0344 

.0255 

.0196 

"                 " 

Butyl      .     .     . 

.0424 

.0324 

.0247 

.0190 

.0150 

"                 " 

Ethyl      .     .     . 

.0150 

.OI22 

.OIO2 

.0085 

.0072 

Gartenmeister. 

Isobutvl      .     . 

.0580 

.O4II 

.0301 

.0223 

.0170 

" 

Isopropyl   .     . 

•0338 

.O248 

.0185 

.0140 

.0108 

" 

Methyl  .     .     . 

.0073 

.0062 

.0054 

.0047 

.0041 

u 

Propyl   .     .     . 

.0293 

.0227 

.0179 

.0142 

.0115 

" 

Aldehyde  ... 

oo^7 

OO77 



_ 

Rellstab. 

Aniline  .... 

J/ 

OAAO 

.0189 

\V  i  i  k.  3,n  dcr. 

Benzene 

OO71 

.0064 

C 

.0048 

Benzoates  :  Ethyl  .     .     . 

•^-KJ/  j 
.0265 

.0217 

.0174 

.0146 

.0124 

Rellstab. 

Methyl    .     . 

.0231 

.0196 

.0160 

.0134 

.0115 

" 

Bromides  :  AIM    .     .     . 

.OO6I 

•°°53 

.0048 

.0045 

.0041 

Pribram  &  Handl. 

Ethyl    .     .     . 
Ethylene  .     . 
Carbon  disulphide      .     . 

.0043 

.0037 
.0169 
.0036 

•0035 
.0149 

•o°35 

.0034 

- 

«<                 n 
Wijkander. 

Carbon  dioxide  (liquid)  . 

.0008 

.0007 

.0005 

— 

Warburg  &  Babo. 

Chlorides:  Allyl     .     .     . 

.0039 

.0036 

•0033 

_ 

_ 

Pribram  &  Handl. 

Ethylene  .     . 

.0083 

.0072 

.0063 

.0056 

<t                        « 

Chloroform   

.0064 

OO  C7 

.00^2 

.0046 

OO/I  "* 

U                                  t( 

Ether    

.OO26 

'0027 

ww  j 
.0021 

.ww^j-v-/ 

_  J 

«                   « 

Ethyl  sulphide    .... 

.0048 

.0043 

.0039 

•0035 

.0032 

«            « 

Iodides:  Allyl   .... 

.0080 

.OO72 

.0065 

.0059 

•°°53 

(«                   « 

Ethyl  .... 

.0064 

.0057 

.0052 

.0048 

.0044 

«                   « 

Metaxylol  

.0075 

.0066 

.0058 

.0052 

.0047 

<«                « 

Nitro  benzene    .... 

.O2O3 

.0170 

.0144 

.0124 

«                                  1C 

"      butane      .... 

.0119 

.OIO3 

.0089 

.0078 

.0069 

(<                « 

"      ethane 

.0080 

.OO7I 

.0064 

.0057 

OO  C2 

u                       « 

"      propane    .... 

.0099 

.ww/ 
.0087 

•  wwvyif. 

.0077 

:oo6i 

" 

"      toluene      .... 

•0233 

.0190 

.0159 

.0136 

«(                   « 

Propyl  aldehyde     .     .     . 

.0047 

.OO4I 

.0036 

•0033 

- 

<«                   « 

Toluene                    .     .     . 

.0068 

.0059 

.0052 

.0047 

.0042 

4*                                  4* 

*  Calculated  from  the  specific  viscosities  given  in  Landolt  &  Boernstein's  "  Phys.  Chem.  Tab."  p.  289  et  seq.,  on 
the  assumption  that  the  coefficient  for  water  at  o°  C.  is  .0178. 
t  For  inorganic  acids,  see  Solutions. 

SMITHSONIAN  TABLES. 

139 


TABLE  156. 


VISCOSITY  OF  SOLUTIONS, 


This  table  is  intended  to  show  the  effect  of  change  of  concentration  and  change  of  temperature  on  the  viscosity  of 
solutions  of  salts  in  water.  The  specific  viscosity  X  loo  is  given  for  two  or  more  densities  and  for  several  tem- 
peratures in  the  case  of  each  solution,  /u.  stands  for  specific  viscosity,  and  t  for  temperature  Centigrade. 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

V- 

t 

> 

t 

r 

' 

- 

t 

Authority. 

BaCl2 

7.6o 

_ 

77-9 

10 

44-o 

3° 

35-2 

5? 

_ 

_ 

Sprung. 

M 

15.40 

- 

86.4 

u 

56.0 

39-6 

- 

- 

" 

" 

24-34 

- 

100.7 

a 

66.2 

" 

47-7 

" 

- 

- 

" 

Ba(N08)2 

2.98 

I.O27 

62.0 

'5 

51-1 

25 

42.4 

35 

34-8 

45 

Wagner. 

u 

5-24 

'    I-05I 

68.1 

(i 

54-2 

u 

44.1 

36-9 

" 

CaCl2 

I5-I7 

_ 

110.9 

IO 

7i-3 

3° 

5°-3 

5° 

_ 

_ 

Sprung. 

" 

31.60 

— 

272.5 

" 

177.0 

" 

124.0 

M 

— 

- 

" 

" 

39-75 

- 

670.0 

" 

379-o 

" 

245-5 

U 

- 

- 

" 

u 

44.09 

„      - 

- 

- 

593-  1 

u 

363-2 

(f 

- 

- 

" 

Ca(N03)2 

17-55 

I.I7I 

93-8 

'5 

74-6 

25 

60.0 

35 

49-9 

45 

Wagner. 

" 

30.10 

1.274 

144.1 

M 

112.7 

" 

90-7 

" 

75-1 

" 

" 

" 

40.13 

1.386 

242.6 

" 

217.1 

" 

156-5 

u 

128.1 

(4 

" 

CdCl2 

11.09 

I.I09 

77-5 

15 

60.5 

25 

49.1 

35 

40.7 

45 

« 

« 

16.30 
24.79 

1.181 
1.320 

88.9 
104.0 

« 

70.5 
80.4 

(i 

Hi 

47-2 
53-6 

« 

Cd(N03)2 

7.81 

1.074 

61.9 

15 

50.1 

25 

41.1 

35 

34-o 

45 

a 

« 

15.71 
22.36 

I-I59 
1.241 

71.8 
85.1 

69.0 

« 

48.8 
57-3 

47-5 

M 

t( 

CdS04 

7.14 

i.  068 

78.9 

15 

61.8 

25 

49-9 

35 

41-3 

45 

« 

" 

14.66 

1.159 

96.2 

72.4 

58.1 

48.8 

" 

" 

22.01 

1.268 

120.8 

(4 

91.8 

" 

73-5 

" 

60.  i 

" 

" 

CoCl2 

7-97 

1.081 

83.0 

15 

65-1 

25 

53-6 

35 

44-9 

45 

« 

a 

14.86 
22.27 

1.161 
1.264 

1  1  1.  6 
161.6 

M 

126.6 

73-7 
101.6 

85'.6 

M 
M 

M 
M 

Co(N03)2 

8.28 

1-073 

74-7 

15 

57-9 

25 

48.7 

35 

39-8 

45 

« 

" 

15.96 

1.144 

87.0 

69.2 

*• 

55-4 

44-9 

" 

" 

24-53 

1.229 

110.4 

" 

88.0 

" 

7!-5 

* 

59-i 

" 

" 

CoS04 

7.24 
14.16 

.086 
-'59 

86.7 
117.8 

'5 

68.7 
95-5 

2.? 

55.0 
76.0 

35 

6i.'7 

45 

U 

" 

21.17 

.240 

193.6 

M 

146.2 

" 

113.0 

H 

89.9 

M 

" 

CuCl2 

12.01 

.104 

87.2 

15 

67.8 

25 

55.1 

35 

45-6 

45 

« 

M 

2I-35 

.215 

121.5 

u 

95-8 

77-0 

63.2 

" 

" 

33-03 

•331 

178.4 

" 

137.2 

" 

107.6 

" 

87.1 

M 

M 

Cu(N03)2 

18.99 

.177 

97-3 

15 

76.0 

25 

61.5 

35 

51.3 

45 

« 

" 

26.68 

.264 

126.2 

98.8 

« 

80.9 

u 

68.6 

" 

" 

46.71 

•536 

382.9 

" 

283.8 

« 

215-3 

" 

172.2 

M 

" 

CuSO4 

6.79 

•055 

79-6 

15 

61.8 

25 

49-8 

35 

41.4 

45 

« 

" 

12.57 

•"5 

98.2 

74-o 

59-7 

52.0 

" 

" 

a 

17.49 

.163 

124.5 

" 

96.8 

" 

75-9 

" 

61.8 

u 

" 

HC1 

8.14 

•037 

71.0 

15 

57-9 

25 

48-3 

35 

40.1 

45 

(t 

" 

16.12 

.084 

80.0 

66.5 

" 

48.1 

H 

(t 

H 

23.04 

.114 

91.8 

" 

79-9 

M 

65-9 

11 

" 

H 

HgCl2 

0.23 

1.023 

_ 

_ 

58-5 

20 

46.8 

3f 

38-3 

40 

« 

" 

3-55 

'•033 

76.75 

IO 

59-2 

46.6 

38.3 

SMITHSONIAN  TABLES. 


I4O 


VISCOSITY   OF   SOLUTIONS. 


TABLE  156 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

<* 

t 

* 

t 

> 

t 

- 

• 

Authority. 

HN03 

8-37 

1.067 

66.4 

15 

54-8 

25 

45-4 

35 

37-6 

45 

Wagner. 

M 

I2.2O 

1.116 

69-5 

57-3 

47-9 

40.7 

" 

U 

28.31 

1.178 

80.3 

" 

65.5 

" 

54-9 

" 

46.2 

" 

" 

H2SO4 

7.87 

1.065 

77-8 

15 

61.0 

25 

50.0 

35 

41.7 

45 

« 

" 

I5-50 

I.I30 

95-1 

" 

75-o 

60.5 

(4 

49.8 

" 

« 

23-43 

1.200 

122.7 

* 

95-5 

" 

77-5 

«« 

64-3 

M 

" 

KC1 

IO.23 
22.21 

- 

70.0 
70.0 

IO 

46.1 
48.6 

30 

36-4 

* 

- 

- 

Sprung. 

M 

KBr 

I4.O2 

_ 

67.6 

10 

44-8 

3p 

32.1 

5° 

_ 

_ 

u 

u 

23.16 

- 

66.2 

" 

44-7 

33-2 

M 

- 

- 

" 

" 

34-64 

- 

66.6 

" 

47-o 

" 

35-7 

" 

- 

- 

" 

KI 

8.42 

_ 

.69-5 

10 

44.0 

30 

3r.3 

5° 

_ 

_ 

« 

" 

I7.OI 

— 

65-3 

" 

42.9 

31-4 

H 

— 

— 

" 

" 

33-03 

- 

61.8 

" 

42.9 

" 

324 

M 

- 

- 

H 

u 

45-98 

54-oo 

- 

63.0 
68.8 

« 

45-2 
48.5 

« 

35-3 
37-6 

« 

- 

- 

« 

KClOg 

3-51 

- 

71.7 

IO 

44-7 

30 

31.5 

5? 

_ 

- 

« 

" 

5-69 

— 

— 

* 

45-o 

" 

314 

U 

— 

— 

" 

KN03 

6.32 

- 

70.8 

10 

44.6 

3p 

31.8 

50 

- 

- 

« 

u 

12.19 

— 

68.7 

II 

44-8 

32-3 

u 

— 

— 

" 

" 

17.60 

- 

68.8 

" 

46.0 

a 

33-4 

M 

- 

- 

" 

K2S04 

5-r7 

_ 

77-4 

IO 

48.6 

3p 

34-3 

5f 

_ 

_ 

« 

" 

9-77 

- 

81.0 

" 

52.0 

36-9 

— 

— 

M 

K2CrO4 

n-93 

_ 

75-8 

IO 

62.5 

3f 

41.0 

40 

- 

- 

H 

« 

19.61 

— 

85-3 

" 

68.7 

47-9 

" 

— 

— 

" 

H 

24.26 

I-233 

97.8 

" 

74-5 

" 

" 

— 

— 

Slotte. 

" 

32.78 

109.5 

M 

88.9 

" 

62.6 

" 

- 

- 

Sprung. 

K2Cr2O7 

4.71 

1.032 

72.6 

10 

55-9 

20 

45-3 

30 

37-5 

4p 

Slotte. 

M 

6.97 

1.049 

73-1 

" 

56-4 

it 

45-5 

37-7 

LiCl 

7.76 

_ 

96.1 

IO 

59-7 

3° 

41.2 

5° 

- 

- 

Sprung. 

« 

— 

121.3 

II 

75-9 

" 

52.6 

" 

— 

— 

" 

M 

26.93 

- 

229.4 

M 

142.1 

" 

98.0 

" 

— 

— 

«« 

Mg(N08)2 

18.62 
34-19 

I.IO2 
I.2OO 

99-8 
213-3 

'.5 

8,.3 

1644 

25 

66.5 
132.4 

» 

56.2 
109.9 

45 

Wagner. 

M 

" 

39-77 

1.430 

u 

25O.O 

" 

191.4 

" 

158-1 

MgSO4 

4.98 

- 

96.2 

10 

59-o 

30 

40.9 

50 

- 

- 

Sprung. 

M 

9-5° 

— 

130.9 

" 

77-7 

" 

53-o 

" 

— 

— 

" 

19.32 

- 

302.2 

" 

166.4 

M 

1  06.0 

U 

— 

- 

M 

MgCrO4 

12.31 

21.86 

1.089 
.164 

111.3 
167.1 

IO 

84.8 
I25-3 

20 

67.4 
99-o 

3? 

55-0 
794 

4p 

Slotte. 

H 

27.71 

.217 

232.2 

H 

172.6 

" 

133-9 

* 

106.6 

MnCl2 

8.01 

.096 

92.8 

15 

71.1 

25 

57-5 

35 

48.1 

45 

Wagner. 

i  £.615 

.196 

130.9 

104.2 

" 

84.0 

" 

68.7 

" 

M 
H 

30-33 
40.13 

•337 
•453 

256-3 
537-3 

« 

193.2 
393-4 

« 

300.4 

." 

123.7 
246.5 

" 

M 

SMITHSONIAN  TABLES. 


TABLE   156. 


VISCOSITY   OF   SOLUTIONS. 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

* 

t 

> 

t 

« 

t 

- 

t 

Authority. 

Mn(NO3)2 
u 

'8-31 
29.60 

49-3  * 

1.148 
1.506 

96.0 

167.5 
3968 

15 

76.4 

126.0 
301.1 

it 

64.5 
104.6 

22I.O 

35 
u 

188^8 

t5 

H 

Wagner. 

u 

MnSO4 

"•45 

I.I47 

129.4 

15 

98.6 

25 

I78'? 

35 

63-4 

45 

« 

" 

18.80 

1.251 

228.6 

" 

172.2 

107.4 

« 

" 

22.08 

1.306 

661.8 

« 

474-3 

" 

347-9 

" 

266.8 

" 

" 

NaCl 

7-95 

_ 

82.4 

IO 

52.0 

3f 

31.8 

5f 

_ 

_ 

Sprung. 

M 

I4-31 

— 

94-8 

" 

60.  i 

36-9 

— 

— 

" 

(I 

23.22 

- 

128.3 

" 

79-4 

" 

47-4 

" 

- 

- 

" 

NaBr 

9-77 

_ 

75-6 

10 

48.7 

3f 

34-4 

5f 

_ 

_ 

u 

" 

18.58 

— 

82.6 

" 

53-5 

38.2 

— 

— 

" 

" 

27.27 

— 

95-9 

" 

61.7 

M 

43-8 

u 

- 

- 

" 

Nal 

8.83 

- 

73  i 

IO 

46.0 

3° 

32-4 

5° 

_ 

_ 

u 

" 

17-15 

— 

73-8 

a 

47-4 

33-7 

u 

— 

_ 

II 

ii 

— 

86.0 

" 

55-7 

" 

40.6 

" 

— 

_ 

H 

" 

55-47 

- 

157-2 

" 

96.4 

" 

66.9 

" 

- 

- 

11 

NaC103 

11.50 

_ 

78.7 

10 

50.0 

30 

35-3 

50 

_ 

_ 

« 

u 

20.59 

— 

88.9 

" 

56-8 

40.4 

— 

— 

" 

" 

33-54 

— 

I2I.O 

" 

75-7 

II 

53-o 

" 

- 

- 

M 

NaNO8 

7-25 

_ 

75-6 

IO 

47-9 

3° 

33-8 

5° 

_ 

_ 

« 

" 

I2-35 

— 

81.2 

" 

51.0 

36.1 

— 

_ 

" 

M 

18.20 

- 

87.0 

M 

55'9 

" 

39-3 

"  ' 

- 

- 

M 

" 

3l-SS 

— 

121.  2 

'" 

76.2 

" 

53-4 

" 

— 

- 

" 

Na2SO4 

4.98 

- 

96.2 

10 

59-o 

3f 

40.9 

5° 

- 

_ 

" 

" 

95° 

— 

130.9 

" 

77-7 

53-° 

— 

— 

It 

" 

14.03 

— 

187-9 

II 

107.4 

II 

71.1 

" 

— 

— 

" 

" 

19.32 

- 

302.2 

" 

166.4 

" 

1  06.0 

" 

- 

- 

H 

Na2CrO4 

5.76 
10.62 

1.058 
1.  112 

85.8 
103-3 

10 

66.6 
79-3 

20 

53-4 
63-5 

If 

43-8 

40 

Slotte. 

H 

" 

14.81 

I.l64 

127-5 

u 

97.1 

" 

77-3 

M 

63.0 

" 

11 

NH4C1 

3.67 

- 

71-5 

IO 

45-° 

3° 

3i.9 

50 

_ 

_ 

Sprung. 

M 

8.67 

— 

69.I 

" 

45-3 

" 

32.6 

" 

— 

- 

" 

" 

15.68 

- 

67-3 

ii 

46.2 

M 

34-o 

" 

- 

- 

M 

" 

23-37 

- 

67-4 

" 

47-7 

" 

36.1 

u 

- 

- 

" 

NH4Br 

1597 

_ 

65.2 

10 

43-2 

3f 

3T-5 

50 

_ 

_ 

« 

« 

3$ 

- 

62.6 
62.4 

I 

43-3 
44.6 

32.2 
34-3 

» 

- 

- 

" 

NH4NO3 

597 

- 

69.6 

IO 

44-3 

3° 

31.6 

5° 

_ 

_ 

« 

" 

12.19 

— 

66.8 

" 

44-3 

M 

3T-9 

" 

— 

— 

li 

" 

27.08 

- 

67.0 

" 

47-7 

" 

349 

u 

- 

- 

M 

" 

37.22 

— 

71.7 

" 

51.2 

" 

38.8 

u 

— 

— 

" 

" 

49-83 

- 

81.1 

" 

63-3 

« 

48.9 

" 

- 

- 

It 

(NH4)2S04 

8.10 

_ 

107.9 

10 

52-3 

30 

37-o 

5f 

_ 

_ 

U 

" 

15-94 

— 

1  20.  2 

M 

60.4 

M 

43-2 

— 

— 

" 

25-51 

148.4 

(I 

74-8 

II 

54-i 

u 

" 

: 

SMITHSONIAN  TABLES. 


I42 


VISCOSITY   OF   SOLUTIONS. 


TABLE  156, 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

M 

t 

* 

t 

X 

t 

- 

' 

Authority. 

(NH4)2Cr04 

10.52 

1.063 

79-3 

10 

62.4 

20 

_ 

_ 

42.4 

40 

Slotte. 

« 

28.04 

1.  1  2O 
I-I73 

88.2 

IOI.I 

« 

70.0 

80.7 

«'« 

si 

3f 

48.4 
56-4 

- 

«( 

(NH4)2Cr207 

6.85 
13.00 

1.039 
1.078 

72-5 
72.6 

IO 

56.3 

57-2 

20 

45-8 
46.8 

3f 

38.0 
39-  ! 

40 

H 

u 

19-93 

I.I26 

77.6 

* 

58.8 

<i 

48.7 

" 

40.9 

" 

(1 

NiCl2 

n-45 
22.69 

I.IO9 
1.226 

90.4 
140.2 

15 

70.0 
109.7 

25 

111 

» 

48.2 
72.7 

45 

Wagner. 

" 

30.40 

i-337 

229.5 

" 

171.8 

" 

139.2 

" 

111.9 

" 

" 

Ni(N03)2 

16.49 

1.136 

90.7 

y 

70.1 

25 

57-4 

35 

48.9 

45 

U 

!! 

30.01 
40.95 

1.278 
1.388 

135.6 

222.6 

105.9 
169.7 

i( 

128.2 

n 

70.7 
152.4 

M 

(i 

NiSO4 

10.62 

1.092 

94.6 

15 

73-5 

25 

60.  i 

35 

49-8 

45 

« 

" 

18.19 

1.198 

154-9 

119.9 

M 

99-5 

M 

75-7 

4t 

u 

M 

25-35 

1.314 

298.5 

" 

224.9 

" 

" 

152.4 

n 

Pb(N03)2 

17-93 

32.22 

1.179 
1.362 

74-o 
91.8 

» 

72-5 

25 
M 

48-5 
59-6 

35 

40.3 
50.6 

45 

« 

Sr(N03)2 

10.29 
21.19 

1.088 
1.124 

69-3 

87-3 

15 

56.0 
69.2 

25 

45-9 

57-8 

35 

39-i 

48.1 

45 

" 

u 

32.61 

1.307 

116.9 

** 

93-3 

" 

76.7 

" 

62.3 

ZnCl2 

15-33 
23-49 
33-78 

1.146 
1.229 
1-343 

93-6 
111.5 

IS1-? 

is 

72.7 
86.6 
117.9 

25 

57-8 
69.8 
90.0 

35 

48.2 

57-5 
72.6 

45 

» 

Zn(N03)2 

15-95 

1.115 

80.7 

15 

64-3 

I5 

52.6 

35 

43-8 

45 

« 

« 

30.23 

1.229 

104.7 

" 

85-7 

69.5 

57-7 

H 

44-50 

1-437 

167.9 

" 

130.6 

« 

105.4 

87.9 

Ci 

ZnS04 

-    7.12 

1.106 

97.1 

15 

79-3 

2S 

62.7 

35 

5r-5 

45 

" 

« 

16.64 

i-!95 

156.0 

" 

118.6 

If 

94.2 

73-5 

M 

23.09 

1.281 

232.8 

177-4 

108.1 

SMITHSONIAN  TABLES. 


143 


TABLE  157. 


SPECIFIC    VISCOSITY.* 


Dissolved  salt. 

Normal  solution. 

£  normal. 

J  normal. 

£  normal. 

Authority. 

1 

Specific 
viscosity. 

>, 

1 

j§.f 

<L>    3 

O-  c/j 

c/j-> 

>, 

1 

Specific 
viscosity. 

4 

1 

il 

'0  o 

sj 

C/T£ 

Acids  :  C12O8      .    . 

1.0562 

I.OI2 

1.0283 

1.003 

1.0143 

I.OOO 

1.0074 

0.999 

Reyher. 

HC1  .     .    . 

I.OI77 

1.067 

1.0092 

1.034 

1.0045 

.017 

1.0025 

I.OO9 

" 

HClOg   .     . 

1.0485 

1.052 

1.0244 

1.025 

I.OI26 

.014 

1.0064 

1.  006 

u 

HNOs    .     . 

1.0332 

1.027 

I.OI68 

I.OII 

1.0086 

.005 

1.0044 

1.003 

<( 

H2SO4    .     . 

1.0303 

I.OOXD 

I.OI54 

1.043 

1.0074 

.022 

1-0035 

1.  008 

Wagner. 

Aluminium  sulphate 

1.0550 

1.406 

1.0278 

I.I78 

1.0138 

.082 

1.0068 

1.038 

H 

Barium  chloride  .     . 

1.0884 

I.I23 

1.0441 

L057 

I.O226 

.026 

1.0114 

I.OI3 

ti 

"        nitrate     .     . 

— 

1.0518 

1.044 

1.0259 

.021 

1.0130 

1.008 

t( 

Calcium  chloride 

1.0446 

1.156 

1.0218 

1.076 

I.OI05 

.036 

1.0050 

I.OI7 

H 

"        nitrate  .     . 

1.0596 

I.II7 

1.0300 

1-053 

1.0151 

.022 

1.0076 

1.008 

« 

Cadmium  chloride  . 

.0779 

I-I34 

1.0394 

1.063 

1.0197 

1.031 

1.0098 

I.O2O 

u 

nitrate     . 

•0954 

I.I65 

1.0479 

1.074 

1.0249 

1.038 

1.0119 

I.OI8 

« 

"         sulphate  . 

•0973 

1.348 

1.0487 

l-*S7 

1.0244 

1.078 

I.OI2O 

I-°33 

" 

Cobalt  chloride   .    . 

•0571 

I.2O4 

1.0286 

1.097 

1.0144 

1.048 

1.0058 

1.023 

« 

"      nitrate      .     . 

.0728 

I.I66 

1.0369 

1-075 

1.0184 

1.032 

1.0094 

1.018 

H 

"      sulphate  .    . 

.0756 

2-354 

1.0383 

1.160 

1.0193 

1.077 

I.OIIO 

1.040 

« 

Copper  chloride  .     . 

.0624 

1.205 

1.0313 

1.098 

.0158 

1.047 

1.0077 

1.027 

« 

"        nitrate    .     . 

•°75S 

1.179 

1.0372 

1.080 

.0185 

1.040 

1.0092 

1.018 

(4 

"        sulphate 

.0790 

i-358 

1  .0402 

1.160 

.0205 

1.080 

1.0103 

1.038 

" 

Lead  nitrate    .     .     . 

.1380 

I.IOI 

0.0699 

1.042 

•0351 

1.017 

1.0175 

1.007 

(( 

Lithium  chloride 

.0243 

1.142 

1.0129 

i.  066 

.0062 

1.031 

1.0030 

I.OI2 

« 

"        sulphate     . 

•0453 

1.290 

1.0234 

i.i37 

.0115 

1.065 

1.0057 

1.032 

" 

Magnesium  chloride 

I-I37S 

I.20I 

1.0188 

1.094 

.0091 

1.044 

1.0043 

I.O2I 

« 

"           nitrate  . 

1.0512 

I.I7I 

1.0259 

1.082 

.0130 

1.040 

1.0066 

1.020 

" 

"           sulphate 

1.0584 

L367 

1.0297 

1.164 

.0152 

1.078 

1.0076 

1.032 

a 

Manganese  chloride 

1*0513 

1.209 

1.0259 

1.098 

.0125 

1.048 

1.0063 

I.O23 

" 

nitrate   . 

1.0690 

1.183 

1.0349 

1.087 

1.0174 

1.043 

1.0093 

I.O23 

u 

"           sulphate 

1.0728 

1.364 

1.0365 

1.169 

1.0179 

1.076 

1.0087 

1.037 

t( 

Nickel  chloride   .    . 

1.0591 

1.205 

1.0308 

1.097 

1.0144 

1.044 

1.0067 

I.  O2  1 

'K 

"      nitrate.     .     . 

!-0755 

I.ISO 

1.0381 

1.084 

1.0192 

1.042 

1  .0096 

I.OI9 

« 

"       sulphate  .     . 

1-0773 

I.36l 

1.0391 

1.161 

1.0198 

1-075 

1.0017 

1.032 

a 

Potassium  chloride  . 

1.0466 

0.987 

1-0235 

0.987 

1.0117 

0.990 

1.0059 

0-993 

u 

"          chromate 

J-°935 

I.II3 

1.0475 

L053 

1.0241 

I.O22 

I.OI2I 

I.OI2 

u 

nitrate    . 

1.0605 

0-975 

1-0305 

0.982 

1.0161 

0.987 

1.0075 

0.992 

« 

"          sulphate 

1.0664 

1.105 

1-0338 

1.049 

1.0170 

1.  02  1 

1.0084 

1.008 

u 

Sodium  chloride  .     . 

1.0401 

1.097 

1.0208 

.047 

1.0107 

I.O24 

1.0056 

i  .01  3 

Reyher. 

"        bromide  .     . 

1.0786 

1.064 

1.0396 

.030 

1.0190 

I.OI5 

I.OIOO 

i.  008 

" 

"        chlorate 

1.0710 

1.090 

I-°359 

.042 

1.0180 

I.O22 

1.0092 

I.OI2 

0 

"        nitrate    .     . 

I-05S4 

1.065 

1.0281 

.026 

1.0141 

I.OI2 

1  .007  1 

1.007 

tt 

Silver  nitrate  .     .     . 

1.1386 

1.058 

1.0692 

.020 

1.0348 

1.  006 

1.0173 

I.OOO 

Wagner. 

Strontium  chloride  . 

1.0676 

1.141 

1.0336 

.067 

1.0171 

.034 

1.0084 

1.014 

u 

"          nitrate    . 

1.0822 

1.115 

1.0419 

.049 

1.0208 

.024 

1.0104 

I.OII 

" 

Zinc  chloride  .     .     . 

1.0509 

1.189 

1.0302 

.096 

1.0152 

•053 

1.0077 

1.024 

14 

"     nitrate     .     .     . 

1.0758 

1.164 

1.0404 

.086 

1.0191 

•°39 

1  .0096 

1.019 

H 

"    sulphate.     .     . 

1.0792 

1.367 

1.0402 

•173 

1.0198 

.082 

1.0094 

1.036 

*  In  the  case  of  solutions  of  salts  it  has  been  found  (vide  Arrhennius,  Zeits.  fiir  Phys.  Chem.  vol.  i,  p.  285)  that 
the  specific  viscosity  can,  in  many  cases,  be  nearly  expressed  by  the  equation  p  =  (*.{";  where  ju.t  is  the  specific  viscosity 
for  a  normal  solution  referred  to  the  solvent  at  the  same  temperature,  and  n  the  number  of  gramme  molecules  in  the 
solution  under  consideration.  The  same  rule  may  of  course  be  applied  to  solutions  stated  in  percentages  instead  of 
gramme  molecules.  The  table  here  given  has  been  compiled  from  the  results  of  Reyher  (Zeits.  fiir  Phys.  Chem.  vol.  2, 
p.  749)  and  of  Wagner  (Zeits.  fiir  Phys.  Chem.  vol.  5,  p.  31)  and  illustrates  this  rule.  The  numbers  are  all  for  25°  C. 

SMITHSONIAN  TABLES. 

144 


TABLE  158. 


VISCOSITY  OF  CASES  AND  VAPORS. 


The  values  of  p  given  in  the  table  are  io6  times  the  coefficients  of  viscosity  in  C.  G.  S.  units. 


Substance. 

Temp. 

M 

Authority. 

Substance. 

Temp. 

M 

Authority. 

Acetone  .... 

18.0 

78 

Puluj. 

Carbon  dioxide     . 

1  2.8 

147 

Schumann. 

"            " 

IOO.O 

208 

" 

Air      

o.o 

17-7 

Thomlinson. 

o.o 

1  68 

Obermeyer. 

Carbon  monoxide 

0.0 

163 

Obermeyer. 

16  7 

Puluj. 

J.  \J.  / 

Chlorine      .    .     . 

o.o 

129 

Graham. 

Alcohol  :  Methyl  . 

66.8 

135 

Stendel. 

" 

2O.O 

147 

M 

Ethyl     . 

78.4 

142 

u 

Normal 

Chloroform      .    . 

17.4 

103 

Puluj. 

propyl 

97-4 

142 

" 

Ether      .... 

1  6.0 

73 

" 

Isopropyl 

82.8 

162 

" 

Normal 

Ethyl  iodide    .     . 

73-3 

216 

Stendel. 

butyl 

116.9 

H3 

" 

Methyl    "... 

44.0 

232 

Isobutyl 

108.4 

144 

u 

Tertiary 

Mercury      .     .    . 

270.0 

489 

Koch* 

butyl 

82.9 

160 

" 

u 

300.0 

u 

. 

33°-° 

f2 

" 

Ammonia     .     .    . 

o.o 

96 

Graham. 

"             .'  .     . 

360.0 

7 

it 

.     .     . 

2O.O 

108 

" 

... 

390.0 

671 

u 

Benzene  .... 

19.0 

79 

Schumann. 

Water     .... 

o.o 

90 

Puluj. 

"         .... 

IOO.O 

118 

" 

"         .... 

16.7 

97 

" 

M 

IOO.O 

132 

L.  Meyer  & 

Carbon  disulphide 

16.9 

99 

Puluj. 

Schumann. 

*  The  values  here  given  were  calculated  from  Koch's  table  (Wied.  Ann.   vol.    19,  p.  869)  by  the  formula 
—  270)]. 


SMITHSONIAN  TABLES. 


145 


TABLE  159. 


COEFFICIENT  OF  VISCOSITY  OF  CASES. 


The  following  are  a  few  of  the  formulze  that  have  been  given  for  the  calculation  of  the  coefficient  of  viscosity  of  gases 

for  different  temperatures. 


Gas. 

Value  of  /*. 

Authority. 

Air     

^0  (i  _|_  .002751  1  —  .00000034  ft) 

Holman. 

.000172  (i  -j-  00273  /) 

O.  E.  Meyer 

« 

OOOl68^  (l  -I-  .OO274./) 

Obermeyer 

Carbon  dioxide    .    . 

<«            « 

/to  (  i  +  -°°37  2  5  *  —  .00000264  /  2  +  .000000004  1  7  /  8) 
.0001414  (I  -f  .00348  /) 

Holman. 
Obermeyer. 

Carbon  monoxide     . 

.0001630  (I  -f-  .00269  1) 

« 

Ethylene      .... 

.0000966  (I  +  -00350  /) 

« 

Ethylene  chloride     . 

.0000935  (I  +  .00381  /) 

M 

Hydrogen    .... 

.0000822  (I  -f-  .00249  /) 

M 

Nitrogen     .... 

.0001635  (I  -f  .00269  /) 

<« 

Nitrous  oxide  (N2O) 

.0001408  (i  +  -00345  1) 

.0001873  (i  -f"  .00283  /) 

<« 
M 

SMITHSONIAN  TABLES. 


146 


TABLE  1  6O. 
DIFFUSION    OF   LIQUIDS  AND   SOLUTIONS   OF   SALTS   INTO  WATER. 

The  coefficient  of  diffusion  as  tabulated  below  is  the  constant  which  multiplied  by  the  rate  of  change  of  concentration 
in  any  direction  gives  the  rate  of  flow  in  that  direction  in  C.  G.  S.  units.  Suppose  two  liquids  diffusing  into  each 
other,  and  let  p  be  the  quantity  of  one  of  them  per  unit  volume  at  a  point  A ,  and  p'  the  quantity  per  unit  volume  at 
an  adjacent  point  £,  and  x  the  distance  from  A  to  B.  Then  if  x  is  small  the  rate  of  flow  from  A  towards  B  is 
equal  to  k  (p  —  p')/x,  where  k  is  the  coefficient  of  diffusion.  Similarly  for  solutions  of  salts  diffusing  into  the  sol- 
vent medium,  p  and  p'  being  taken  as  the  quantities  of  the  salt  per  unit  volume.  The  results  indicate  that  k  depends 
on  the  absolute  density  of  the  solution.  Under  c  will  be  found  the  concentration  in  grammes  of  the  salt  per  100  cu. 
cms.  of  the  solution  ;  under  n  the  number  of  gramme-molecules  of  water  per  gramme-molecule  of  salt  or  of  acid  or 
other  liquid. 


Substance. 

c 

tl 

fcXIO7 

Temp.  C. 

Authority. 

Ammonia    

_ 

16.0 

123 

4-5 

Scheffer* 

Ammonium  chloride  . 

23 

85.0 

123 
135 

4-5 

IO.O 

u 

Schuhmeister.t 

«                    u 

61.0 

17.5 

Scheffer 

Barium  chloride  .... 

_ 

46.0 

76 

8.0 

* 

Calcium  chloride 

- 

13.0 

83 

9.0 

"• 

"             "               ... 

— 

297.0 

74 

9.0 

" 

u            « 

10 

384.0 

79 
79 

9.0 

IO.O 

Schuhmeister. 

Cobalt  chloride  .... 

10 

- 

53 

10.0 

" 

Copper       " 

10 

— 

5° 

IO.O 

" 

Copper  sulphate 
Hydrochloric  acid 

IO 

~0 

IO.O 
0.0 

Scheffer. 

"          ... 

— 

9.8 

215 

o.o 

"           ... 

— 

14.1 

195 

o.o 

M 

— 

27.1 

176 

o.o 

M 

- 

129.5 

161 

0.0 

"               ... 

— 

7.2 

3°9 

II.O 

"               ... 

_ 

27.6 

245 

II.O 

"               ... 

- 

69.4 

234 

II.O 

Lead  nitrate         .... 

: 

108.4 
136.0 

2I3 
76 

II.O 
I2.O 

Lithium  chloride 

.14 

5H-o 

82 
81 

I2.O 
IO.O 

Schuhmeister. 

"      bromide 

20 

— 

93 

IO.O 

" 

"            "                ... 

38 

- 

100 

IO.O 

" 

"      iodide    .... 

17 

- 

93 

IO.O 

M 

Magnesium  sulphate   . 

IO 

45.0 

32 
32 

IO.O 

5-5 

H 

Scheffer. 

"                "... 

_ 

184.0 

37 

5-5 

" 

"                "... 

— 

30.0 

3i 

IO.O 

«                "... 

_ 

248.0 

IO.O 

" 

Potassium  chloride     . 

_ 

32.0 

98 

7.0 

M 

u                        u 

10 

107.0 

1  06 
127 

7.0 

IO.O 

Schuhmeister. 

"                "... 

30 

- 

147 

IO.O 

4< 

"          bromide     . 

10 

— 

I31 

IO.O 

«                "... 

3° 

— 

144 

IO.O 

"          iodide 

IO 

— 

130 

IO.O 

3° 

- 

IO.O 

" 

u                       «                t  ;- 

90 

— 

168 

IO.O 

"           nitrate 

15 

— 

93 

IO.O 

"          sulphate     . 

13 

- 

87 

IO.O 

"( 

Sodium  chloride 

IO 

— 

97 

IO.O 

t( 

3° 

— 

106 

IO.O 

bromide 

3° 

- 

99 

IO.O 

iodide     .... 

15 

— 

93 

IO.O 

3° 

— 

IOO 

IO.O 

nitrate    .        .        . 

IO 

- 

69 

IO.O 

1 

carbonate 

13 

- 

45 

IO.O 

sulphate         *        »    -    « 
Nitric  acid  .         ....••. 

10 

2.9 

76 
225 

IO.O 

9.0 

Scheffer. 

__ 

7-3 

234 

9.0 

«          <t 

_ 

35-° 

206 

9.0 

" 

«          « 

_ 

426.0 

200 

9.0 

" 

Sulphuric  acid    .... 

- 

18.8 

124 

8.0 

u 

<<          «                         .        . 

— 

125.0 

"5 

5 

"          " 

_ 

686.0 

132 

9.0 

M               « 

_ 

°-5 

13.0 

MM                                       > 

- 

35-Q 

144 

13.0 

*  "  Z.  fur  Phys.  Chem."  2,  p.  39°- 

t  "  Wien 

.  Akad.  Ber. 

'  vol.  79,  2. 

Abth.  p.  603. 

SMITHSONIAN    TABLES. 

147 


TABLE  161. 


DIFFUSION    OF   CASES   AND   VAPORS. 


Coefficients  of  diffusion  of  vapors  in  C.  G.  S.  units.     The  coefficients  are  for  the  temperatures  given  in  the  table  and 
a  pressure  of  76  centimetres  of  mercury.* 


Vapor. 

Temp.  C. 

0 

Jet  for  vapor 
diffusing  into 
hydrogen. 

kt  for  vapor 
diffusing  into 
air. 

kt  for  vapor 
diffusing  into 
carbon  dioxide. 

Acids  :  Formic         .                 .        , 

O.O 

o-S^1 

O.I3I5 

0.0879 

<t 

65.4 

0.7873 

0-2035 

0.1343 

•         •         .         • 

84-9 

0.8830 

0.2244 

0.1519 

Acetic          .... 

O.O 

0.4040 

0.1061 

0.0713 

"              .... 

65.5 

0.6211 

0.1578 

0.1048 

«< 
Isovaleric    .... 

98.5 

O.O 

0.7481 

0.21  18 

0.1965 
0-0555 

0.1321 
0-0375 

. 

98.0 

0-3934 

0.1031 

0.0696 

Alcohols:  Methyl    .... 

0.0 

0.5001 

0.1325 

0.0880 

"... 

25.6 

0.6015 

0.1620 

0.1046 

"        •         .         .         . 

49.6 

0.6738 

0.1809 

0.1234 

Ethyl        .... 

0.0 

0.3806 

0.0994 

0.0693 

. 

40.4 

0.5030 

0.1372 

0.0898 

ii 

66.9 

0-543° 

o.i475 

O.IO26 

Propyl     .... 

0.0 

0-3I53 

0.0803 

0-0577 

. 

66.9 

0.4832 

0.1237 

0.0901 

«< 

83-5 

0-5434 

0.1379 

0.0976 

Butyl       .... 

0.0 

0.2716 

0.068  1 

0.0476 

it 

99.0 

0-5045 

0.1265 

0.0884 

Amyl       .         .        .        .     ' 

0.0 

0-2351 

0.0589 

0.0422 

"           •  '      .         .         . 

99.1 

0.4362 

0.1094 

0.0/84 

Hexyl      .... 

O.O 

0.1998 

0.0499 

0-0351 

« 

99.0 

0.3712 

0.0927 

0.0651 

O.O 

o.  20,40 

0.07  ci 

O.O527 

IQ.Q 

J/T" 

0.  74.OQ 

/  j* 
0.0877 

"*"**j*/ 

0.0609 

« 

S    S 

4^.0 

^  OT"    -7 
O.'^QQ'? 

w.wvj  j  i 

O.IOII 

0.071  c 

Carbon  disulphide    .... 

TO*V 

0.0 

O^-?O 

0.3690 

0.0883 

/    j 
0.0629 

«              « 

19.9 

0.4255 

0.1015 

0.0726 

«              « 

32.8 

0.4626 

O.II2O 

0.0789 

Esters  :  Methyl  acetate    . 

O.O 

0-3357 

0.0852 

0.0572 

"            "... 

20.3 

0.3928 

O.IOI3 

0.0679 

Ethyl          "          .         .         . 

O.O 

0-2373 

0.0630 

0.0450 

«              « 

46.1 

0.3729 

0.0970 

0.0666 

Methyl  butyrate  .         .        . 

0.0 

0.2422 

0.0640 

0.0438 

«             «c 

92.1 

0.4308 

O.II39 

0.0809 

Ethyl                    !         ! 

0.0 

0.2238 

0-0573 

0.0406 

«               « 

96.5 

0.4112 

0.1064 

0.0756 

"      valerate     .        . 
«          «t 

O.O 

97.6 

0.2050 
0.3784 

0.0505 
0.0932 

0.0366 
0.0676 

Ether        .        .        .        .        .      V 

O.O 

0.2060 

0.0771: 

0.0552 

IQ.Q 

s 

O.^AIO 

/    /   J 

O.oSo  7 

0.0636 

Water       .        .        .        . 

s  s 

O.O 

w*  J*T*  ** 

0.6870 

;?O 

0.1980 

0.1310 

40.  c 

I.OOOO 

0.2827 

o.  1811 

« 

'Vy  •  j 
02.  4 

1.1704 

o.  74  1;  i 

0.2184 

Jf*»*r 

/  ^T" 

O^  j 

w   ~v)     T" 

*  Taken  from  Winkelmamrs  papers  (Wied.  Ann.  vols.  22,  23,  and  26).  The  coefficients  for  o°  were  calculated 
by  Winkelmann  on  the  assumption  that  the  rate  of  diffusion  is  proportional  to  the  absolute  temperature.  According 
to  the  investigations  of  Loschmidt  and  of  Obermeyer  the  coefficient  of  diffusion  of  a  pas,  or  vapor,  at  o°  C.  and  a 
pressure  of  76  centimetres  of  mercury  may  be  calculated  from  the  observed  coefficient  at  another  temperature  and 

pressure  by  the  formula  &0  =  &T  (-^-)    — »  where   T  is  temperature  absolute  and  p  the  pressure  of  the  gas.     The 

exponent  n  is  found  to  be  about  1.75  for  the  permanent  gases  and  about  2  for  condensible  gases.  The  following 
are  examples:  Air  — CO2,  «=  1.968;  CO,—  N2O,  «  =  2.oS;  CO2— H,  «=i.742;  CO  — O,  «  =  1.785;  H  — Or 
«=i.7555  O  —  N,  » =31.792.  Winkelmann's  results,  as  given  in  the  above  table,  seem  to  give  about  2  for  vapors, 
diffusing  into  air,  hydrogen  or  carbon  dioxide. 

SMITHSONIAN  TABLES. 

148 


TABLE  162. 
COEFFICIENTS   OF    DIFFUSION    FOR   VARIOUS   CASES   AND   VAPORS.* 


Gas  or  vapor  diffusing. 

Gas  or  vapor  diffused  into. 

Temp. 
C.° 

Coefficient 
of  diffusion. 

Authority. 

Air     

Carbon  dioxide    . 

0 

0.1343 

Obermayer. 

"..... 

Oxygen 

0 

0.1775 

" 

Carbon  dioxide  . 

Air        .... 

O 

0.1423 

Loschmidt. 

"            "... 

14 

O 

0.1360 

Waitz. 

"            "... 

Carbon  monoxide 

O 

0.1405 

Loschmidt. 

"            "... 

"            " 

O 

0.1314 

Obermayer. 

"            "... 

Ethylene 

O 

O.I  006 

" 

"            "... 

Hydrogen 
Methane 

0 
0 

0.5437 
0.1465 

" 

"            "... 

Nitrous  oxide 

0 

0.0983 

Loschmidt. 

"            "... 

Oxygen 

O 

0.1802 

" 

Carbon  disulphide 

Air        .... 

O 

0.0995 

Stefan. 

Carbon  monoxide 

Carbon  dioxide     . 

0 

0.1314 

Obermayer. 

u                     « 

Ethylene        «        . 

0 

0.1164 

" 

U                              « 

Hydrogen 

0 

0.6422 

Loschmidt. 

"                "                 . 

Oxygen 

0 

o.i  802 

M 

«                     u 

"                ... 

O 

0.1872 

Obermayer. 

Ether         .        .        .'        ! 

Air        .... 

O 

0.0827 

Stefan. 

Hydrogen  .... 

Hydrogen 
Air         .... 

O 
0 

0.3054 

0.6340 

a 

Obermayer. 

. 

Carbon  dioxide     . 
"     monoxide 

O 
O 

o-5384 
0.6488 

u 

.... 

Ethane  .... 

O 

0-4593 

" 

. 

Ethylene 

0 

0.4863 

" 

.         .         • 

Methane 

0 

0.6254 

" 

H 

Nitrous  oxide 

O 

0-5347 

14 

"                 .... 

Oxygen 

O 

0.6788 

" 

Nitrogen     .... 

Oxvgen 

O 

0.1787 

" 

Oxygen       .... 

Carbon  dioxide     . 
Hydrogen 

O 
0 

0.1357 
0.7217 

Loschmidt. 

M 

Sulphur  dioxide 
Water         .... 

Nitrogen 
Hydrogen      . 
Air        .        .        . 

O 
0 

8 

0.1710 
0.4828 
0.2390 

Obermayer. 
Loschmidt. 
Guglielmo. 

"              .... 

"           .... 

18 

0.2475 

" 

. 

Hydrogen      .        . 

18 

0.8710 

*  Compiled  for  the  most  part  from  a  similar  table  in  Landolt  &  Boernstein's  "  Phys.  Chem.  Tab." 

SMITHSONIAN  TABLES. 

149 


TABLE  163. 


OSMOSE, 


The  following  table  given  by  H.  de  Vries*  illustrates  an  apparent  relation  between  the  isotonic  coefficient  t  of  solu- 
tions and  the  corresponding  lowering  of  the  freezing-point  and  the  vapor  pressure.     The  freezing-points  are  taken 
"  Raoul 


on  the  authority  of 


ill,  and  the  vapor  pressures  on  the  authority  of  Tammann. 


Substance. 

Formula. 

Isotonic 
coefficient 
Xioo. 

Molecular 
lowering  of 
the  freezing 
point  X  loo. 

Molecular 
lowering  of 
the  vapor 
pressure 
Xiooo. 

Glycerine     .... 

C3H803 

I78 

171 

_ 

Cane  sugar  .... 

Ci2H22On 

188 

*^5 

— 

Tartaric  acid 

C4H606 

202 

JQC 

188 

Magnesium  sulphate   . 
Potassium  nitrate 

MgS04 
KN03 

196 
300 

192 

308 

'56 
267 

Sodium  nitrate     . 

NaNO3 

300 

337 

296 

Potassium  chloride 

KC1 

287 

336 

313 

Sodium  chloride  . 

NaCl 

3°5 

351 

330 

Ammonium  chloride    . 

NH4CI 

300 

348 

3*3 

Potassium  acetate 

KC2H3O2 

300 

345 

33  I 

Potassium  oxalate 

K2C2O4 

393 

45° 

372 

Potassium  sulphate 

K2SO4 

392 

39° 

351 

Magnesium  chloride    . 
Calcium  chloride 

MgCl2 
CaCl2 

433 
433 

488 
466 

5T3 

TABLE  164. 


OSMOTIC   PRESSURE. 


The  following  numbers  give  the  result  of  Pfeff er's  §  measurement  of  the  magnitude  of  the  osmotic  pressure  for  a  one 
per  cent  sugar  solution.  The  result  was  found  to  agree  with  that  of  an  equal  molecular  solution  of  hydrogen. 
The  value  for  the  hydrogen  solution  is  given  in  the  third  column  of  the  table. 


Temperature 
C» 

Osmotic  pressure 
in  atmospheres. 

0.649(1  -f-  .00367  /) 

6.8 

0.664 

0.665 

J37 

0.691 

0.681 

14.2 

0.671 

0.682 

«$•$ 

0.684 

0.686 

22.O 

0.721 

0.701 

32.0 

0.716 

0.725 

36.0 

0.746 

°-735 

'  "Zeits.  fur  Phys.  Chem."  vol.  2,  p.  427. 

t  The  isotonic  coefficient  is  the  relative  value  of  the  molecular  attraction  of  the  different  salts  for  water  or  the 
relative  value  of  the  osmotic  pressures  for  normal  solutions.  In  the  above  table  the  coefficient  for  KNO3  was  taken 
as  3  arbitrarily  and  the  others  compared  with  it.  The  concentrations  of  different  salts  which  give  equal  osmotic  pres- 
sures are  called  by  Tammann  and  others  isosmotic  concentrations  ;  they  are  sometimes  called  isotonic  concentrations. 
The  reciprocals  of  the  numbers  of  molecules  in  the  isotonic  concentrations  are  called  by  De  Vries  the  isotonic  coeffi- 
cients. 

t  See  also  Tammann,  "  Wied.  Ann."  vol.  34,  p.  315. 

§  Winkelmann's  "  Handbuch  der  Physik,"  vol.  i,  p.  632. 

SMITHSONIAN  TABLES. 

ISO 


TABLE  165. 
PRESSURE   OF   AQUEOUS   VAPOR,   ACCORDING   TO   RECNAULT. 

The  last  four  columns  were  calculated  from  the  data  given  in  the  second  column  and  the  density  of  mercury. 


q 

<u 

it 

sr 

* 

lt 

| 

1 

i 

it 

5f 

* 

! 

i 

u 
M 

u 

o 

3 

ii 

s| 

! 

If 

£ 

o 

CJ 
o 

ei 

|| 

s, 

gi 

«f 

o 

A 

i! 

Is 

i  = 

1*3 

1| 

a 

• 

d, 

e 

h 

E  = 
2  <•> 

•8.C 
l-s 

<£*o 

3   O 

1 

H 

£ 

o 

£ 

£ 

£ 

H 

H 

£ 

O 

1 

£ 

£ 

H 

0 

4.60 

6.254 

0.0890 

0.181 

0.006  1 

32.0 

40 

54-9  T 

74-653 

i.  06  1 

2.162 

0.072 

104.0 

i 

4-94 

6.716 

•0955 

.194 

.0065 

33-8 

41 

57-91 

78.678 

1.  121 

2.280 

.076 

105.8 

2 

5-3° 

7.206 

.1025 

.209 

.0070 

35-6 

42 

61.01 

82.947 

1.216 

2.404 

.080 

107.6 

3 

5.69 

7.736 

.1100 

.224 

.0075 

37-4 

43 

64.35 

87.488 

1.244 

2-533 

.085 

109.4 

4 

6.10 

8.291 

.1180 

.240 

.0080 

39-2 

44 

67-79 

92.165 

I.3I2 

2.669 

.089 

III.  2 

5 

6-53 

8.878 

0.1263 

0.257 

0.0086 

41.0 

45 

7i-39 

97-059 

I.38l 

2.811 

0.094 

H3.0 

6 

7.00 

9-517 

•1354 

.276 

.0092- 

42.8 

46 

75-16 

102.184 

1.454 

2-959 

•099 

II4.8 

7 

7-49 

10.183 

.1452 

•295 

.0099 

44-6 

47 

79.09 

107.528 

'•530 

.IO4 

II6.6 

8 

8.02 

10.904 

-I551 

.316 

.0107 

46.4 

48 

83.20 

113.115 

1.609 

3-276 

.109 

II8.4 

9 

8-57 

11.651 

•  1657 

•338 

.0114 

48.2 

49 

87-50 

118.962 

1.692 

3-444 

.II5 

120.2 

10 

9.17 

12.467 

0.1773 

0-361 

0.012 

50.0 

50 

91.98 

125.05 

1.78 

3-62 

O.I2I 

122  0 

ii 

9-79 

13.310 

.1893 

•386 

.013 

51.8 

51 

96.66 

131.42 

1.87 

3.81 

.127 

123.8 

12 

10.46 
ii.  16 

14.207 
15.173 

.2023 

.412 

.OI4 
.015 

53-6 

55-4 

52 
53 

101.54 
106.64 

1  38.04 
144-98 

1.96 

2.06 

4.00 
4.20 

•134 
.140 

125.6 
1274 

14 

11.91 

16.192 

-2303 

.469 

.016 

57-2 

54 

111.95 

152.20 

2.17 

4.41 

.147 

129.2 

15 

12.70 

17.266 

0.2456 

0.500 

O.OI7 

59° 

55 

117.48 

159-72 

2.27 

4-63 

0.155 

1310 

16 

I3-S4 

18.408 

.2618 

•533 

.018 

60.8 

56 

123.24 

l67-55 

2-39 

4-85 

.163 

132.8 

17 

14.42 

19.605 

.2789 

.568 

.019 

62.6 

57 

129.25 

I75-72 

2.50 

5-09 

.170 

1346 

18 

15.36 

20.883 

.2970 

•605 

.O2O 

64.4 

58 

135.51 

184.23 

2.62 

5-33 

.178 

136.4 

19 

16-35 

22.229 

.3162 

.644 

.022 

66.2 

59 

142.02 

193.08 

2-75 

5-59 

.187 

138.2 

20 

T7-39. 

23-643 

0-3363 

0.685 

0.023 

68.0 

60 

148.79 

202.29 

2.88 

5.86 

0.196 

140.0 

21 

22 

18.50 
19.66 

25.152 
26.729 

•3577 
.3802 

.728 
•774 

.024 
.026 

69.8 
71.6 

61 
62 

I55-84 
163.17 

211.87 
221.84 

3°6 

6.14 
6.42 

.205 
.215 

I4I.8 
143.6 

23 

20.89 

28.401 

.4040 

.822 

.028 

73-4 

63 

170.79 

232.20 

3-3° 

6.72 

.225 

145-4 

24 

22.18 

30.155 

.4289 

•873 

.029 

75-2 

64 

178.71 

242.97 

3-46 

7.04 

•235 

147.2 

25 

23-55 

32.018 

0-4554 

0.927 

0.031 

77.0 

65 

186.95 

254-I7 

3.62 

7-36 

0.246 

149.0 

26 

24.99 

33-975 

•4833 

.984 

•033 

78.8 

66 

195.50 

265.79 

378 

7.70 

.257 

150.8 

27 

26.51 

36.042 

.5126 

1.044 

•034 

80.6 

67 

204.38 

277.87 

3-95 

8.05 

.267 

152.6 

28 

28.10 

38.204 

•5434 

.106 

•037 

82.4 

68 

213.60 

290.40 

4.13 

8.41 

.28l 

1544 

29 

29.78 

40.488 

•5759 

.172 

•039 

84.2 

69 

223.17 

30341 

4-32 

8.79 

•494 

156.2 

30 

3r-55 

42.894 

0.6101 

1.242 

0.042 

86.0 

70 

233.09 

316.90 

4-51 

9.18 

0.306 

I58.O 

31 

33-41 

45-423 

.6461 

•3*5 

.044 

87.8 

71 

243-39 

330.90 

4.71 

9-58 

.320 

I59.8 

32 

35-36 

48.074 

.6838 

•392 

•047 

89.6 

72 

254-07 

345-42 

4.91 

IO.OO 

•334 

161.6 

33 

34 

37-41 
39-57 

50.861 
53-798 

•7234 
•7655 

•473 
-558 

.049 

.052 

91.4 
93-2 

73 
74 

265.15 
276.62 

360.49 
376.o8 

5.12 

5-35 

10.44 
10.89 

-349 
-364 

163.4 
165.2 

35 

41.83 

56.870 

0.810 

1.647 

0.055 

950 

75 

288.52 

392.26 

558 

11.36 

0.380 

167.0 

36 
39 

44.20 
46.69 
49-30 
52-04 

60.093 
63.478 
67.026 
70.752 

.855 
•903 
•954 
1.007 

•740 
•838 
.941 
2.049 

.058 

.068 

96.8 
98.6 
100.4 

IO2.2 

76 
77 
78 
79 

300.84 
313.60 
326.81 
340.49 

409.01 
426.36 
444.32 
462.92 

5.82 
6.06 
6.32 
6.58 

11.84 

12.35 
12.87 
13.40 

•396 
.414 

•430 
.448 

168.8 
170.6 
172.4 
174.2 

SMITHSONIAN  TABLES. 


TABLE  165. 

PRESSURE  OF  AQUEOUS  VAPOR, ACCORDING  TO  RECNAULT. 


a 

0 

n. 
E 

3  £ 

2*0 

Jrammes  per  sq.  I 
centimetre. 

'ounds  per  sq. 
inch. 

1 

f. 

3  E 
2*0 

i 
if 

3   g 

J: 
o 

I 

B 

CJ 
o 
d 
E 

V 

5ressure  :  mm. 
of  mercury. 

Grammes  per  sq. 
centimetres. 

'ounds  per  sq. 
inch. 

3ressure:  inches  1 
of  mercury. 

p 

a  « 

o 

M 
m 
m 

o 

A 

E 

^ 

OH 

w 

if? 

H 

80 

354.64 

482.15 

6.85 

13.96 

0.446 

176.0 

120 

1491.28 

2027.48 

28.85 

58-71 

1.962 

248.0 

81 

369.29 

502.07 

7.14 

14.54 

.486 

177.8 

121 

1  539-25 

2092.70 

29.78 

60.61 

2.025 

249.8 

82 

384.44 

522.67 

7-44 

.506 

179.6 

122 

I588.47 

2159.62 

3°-73 

62.54 

.091 

251.6 

83 

4OO.IO 

543-96 

7-74 

15-75 

.526 

181.4 

123 

1638.96 

2228.26 

31.70 

64.53 

•1S7 

253-4 

84 

416.30 

565.99 

8.05 

16.39 

.548 

183.2 

124 

1690.76 

2298.69 

32-70 

66.56 

•225 

255-2 

85 

433-04 

588.74 

8-37 

17.05 

0.570 

185.0 

125 

1743.88 

2370.91 

33-72 

68.66 

2.295 

257.0 

86 

450-34 

612.26 

8.71 

17.73 

•593 

186.8 

126 

1798.35 

2444.96 

34.78 

70.80 

.366 

258.8 

87 

468.22 

636.57 

9-°5 

18.43 

.616 

188.6 

127 

1854.20 

2520.89 

35.86 

73-00 

.43° 

260.6 

88 

486.69 

661.68 

9.41 

19.16 

.640 

180.4 

128 

1911.47 

2598.76 

36-97 

75-25 

262.4 

89 

505-76 

687.61 

9.78 

19.91 

.665 

192.2 

129 

1970.15 

2678.54 

38.11 

77-57 

•592 

264.2 

90 

525.45 

714.38 

10.16 

20.69 

0.691 

194.0 

130 

2030.28 

2760.29 

39.26 

79-93 

2.671 

266.0 

91 

545-78 

740.31 

10.56 

21.49 

.719 

195.8 

131 

2091.94 

2844.12 

40.47 

•753 

267.8 

92 

566.76 

770.54 

10.95 

22.31 

•746 

197.6 

132 

2I55.03 

2929.89 

41.68 

84^84 

.836 

269.6 

93 

588.41 

799-98 

11.38 

23-17 

•774 

199.4 

T33 

2219,69 

3017.80 

42.93 

87-39 

.921 

271.4 

94 

6IO.74 

830.34 

11.81 

24.04 

.804 

2OI.2 

134 

2285.92 

3107.85 

44.21 

89.99 

3.008 

273.2 

95 

633.78 

861.66 

12.26 

24.95 

0.834 

203.0 

135 

2353-73 

3200.04 

45-52 

92.67 

3-097 

275.0 

96 

657-54 

893-97 

12.71 

25.89 

.865 

204.8 

136 

2423.16 

329443 

46.87 

95-39 

.188 

276.8 

97 

682.03 

927.26 

13.19 

26.85 

.897 

206.6 

2494.23 

3391.06 

48.24 

98.19 

.282 

278.6 

98 

707.28 

961.59 

13.68 

27.85 

•931 

208.4 

138 

2567.00 

3489.99 

49-65 

101.06 

-378 

280.4 

99 

733-31 

996.98 

14.18 

28.87 

•965 

210.2 

139 

2641.44 

359L29 

51.06 

103.99 

-476 

282.2 

100 

760.00 

1033.26 

14.70 

29.92 

I.OOO 

2I2.O 

140 

2717.63 

3694.78 

52.55 

106.99 

3-576 

284.0 

IOI 

787-59 

1070.78 

15-23 

31.01 

.036 

213.8 

141 

2795-57 

3800.75 

54-07 

1  1  0.06 

.678 

285.8 

IO2 

103 

816.01 
845-28 

1109.41 
1149.21 

15-79 
16.35 

32.13 

33.28 

•074 

.112 

215.6 
217.4 

142 
H3 

2875.30 
2956.86 

3909.14 
4020.03 

55-60 

113.20 
116.41 

•783 
.890 

287.6 
289.4 

104 

875-4I 

1190.17 

16.94 

34.46 

.152 

219.2 

144 

3040.26 

413342 

58.79 

119.69 

4.000 

291.2 

105 

1  06 

906.41 
938-3  l 

1232.32 
1275.69 

T7-53 
18.15 

35-69 

36.94 

I-I93 

•235 

221.0 

222.8 

145 

146 

3I25.55 
3212.74 

4249-37 
4367.91 

60.44 
62.13 

123.05 
1  26.48 

4.113 

.227 

293-0 

294.8 

107 

971.14 

1320.32 

18.78 

38.23 

.278 

224.6 

147 

3301.87 

4489.09 

63.86 

129.99 

•344 

296.6 

1  08 

1004.91 

1366.24 

19.44 

39.56 

•322 

226.4 

148 

3392.98 

4612.96 

65.62 

I33-58 

•464 

298.4 

109 

1039.65 

1413-47 

20.  1  1 

40.93 

.368 

228.2 

149 

3486.09 

4739-55 

67.41 

J37-25 

.587 

300.2 

110 

1075-37 

1462.03 

20.80 

42.34 

1.415 

230.0 

150 

3581.2 

4868.9 

69.26 

141.0 

4.712 

302.0 

in 

1  1  1  2.09 

1511.97 

21.51 

43-78 

•463 

231.8 

151 

3678.4 

5001.1 

71.14 

144.8 

.840 

303-8 

112 

1149.83 

1563.26 

22.24 

45-25 

•5r3 

152 

3777-7 

5136-1 

73.06 

148.7 

.971 

305-6 

"3 

1188.61 

1615.99 

22.99 

46.80 

•564 

2354 

3879-2 

5275-0 

75-02 

152-7 

5.104 

3°7-4 

114 

1228.47 

1670.18 

23-76 

48.37 

.616 

237.2 

154 

3982.8 

5414.8 

77-03 

156.8 

.240 

309.2 

115 

1269.41 

1725.84 

24-55 

49.98 

1.670 

239.0 

155 

4088.6 

5558.6 

79.07 

161.0 

S-38o 

311.0 

116 

1783.02 

25-37 

5*-63 

.726 

240.8 

156 

4196.6 

5705-5 

81.22 

165.2 

'.522 

312.8 

117 

1354.66 

1841.74 

26.20 

53-34 

.782 

242.6 

T57 

4306.9 

83.29 

169.6 

.667 

314.6 

118 

1399.02 

1902.05 

27.06 

55.08 

.841 

244.4 

158 

44I9.5 

6008.5 

85-47 

174.0 

.815 

316.4 

119 

1444-55 

.963.95 

27.94 

56.87 

.901 

246.2 

159 

4534-4 

6164.7 

87-69 

178.5 

.966 

318.2 

SMITHSONIAN  TABLES. 


152 


TABLE  165. 
PRESSURE  OF  AQUEOUS  VAPOR, ACCORDING  TO  RECNAULT. 


o 
a 
| 

H 

Pressure:  mm. 
of  mercury. 

Grammes  per  sq.  1 
centimetre. 

ft 

l-s 

•2   C 
OH 

Pressure  :  inches  1 
of  mercury. 

i 

..  .£ 
u  ft 

1 

o 
ft 

1 

o 

ft 

1 

Pressure:  mm. 
of  mercury. 

Grammes  per  sq.  1 
centimetre. 

Pounds  per  sq. 
inch. 

1  Pressure:  inches  1 
of  mercury. 

t 

it 

£ 

o 
d 

i 
h 

160 

4651.6 

6324.2 

89.96 

83.1 

6.120 

20.0 

195 

0519.6 

14302.7 

03-43 

414.1 

3-842 

383-0 

161 

477  i  -3 

6486.8 

92.27 

87.9 

6.278 

21.8 

196 

0746.0 

14609.8 

07.81 

423.1 

4-139 

384-8 

162 
163 

4893.4 
5OI7-9 

6652.8 
6822.2 

97.04 

92.7 
97-6 

6-439 
6.603 

23-6 

25-4 

0975-0 
1209.8 

14921.2 
15240.4 

216.77 

432.1 
441-3 

4.441 
4-749 

386.6 
388.4 

164 

5H5-0 

6994.9 

99-50 

202.6 

6.770 

327.2 

199 

1447-5 

15563.5 

221.37 

450-7 

5.062 

390.2 

165 

5274-5 

7171.1 

O2.OI 

207.7 

6.940 

329.0 

200 

1689.0 

15891.9 

226.04 

460.1 

5.380 

392-0 

1  66 

5406.7 

7350.7 

04.56 

212-9 

7.114 

30.8 

20  1 

1934-4 

16225.5 

230.79 

469.8 

5-703 

3938 

167 
1  68 

169 

5541-4 
5678.8 
5818.9 

7533-9 
7720.7 
7911.1 

07.18 
09.84 
12.53 

218.2 
223.6 
229.1 

7.291 

7.472 
7.656 

332-6 

334-4 
336-2 

202 
203 

20^ 

2183.7 
2437.0 
2694.3 

16564.7 
16908.8 

235-6I 
240.54 
245.49 

479-7 
489.6 

499-8 

6.031 
6.364 
6.703 

395-6 
397-4 
399-2 

170 

5961-7 

8105.2 

15.29 

234.1 

7.844 

338.0 

205 

2955-7 

17614.0 

250.53 

510.1 

7.047 

401.0 

171 

6107.2 

8303.1 

i8.ii 

240.4 

8.036 

339-8 

206 

3221.1 

17974.9 

255.67 

520.5 

17.396 

402.8 

172 
173 
174 

6255-5 
6406.6 
6560.6 

8504.7 
8710.2 
8919.5 

20.98 
23.90 
126.87 

246.3 

2^3 

8.231 
8.430 
8.632 

341.6 
343-4 
345-2 

209 

3490.8 

3764-5 
4042.5 

18341-5 
I87I3-7 
19091.6 

260.88 
266.18 
27I-55 

531-2 
541-9 
552-9 

I7-751 
18.111 

18.477 

404.6 
406.4 
408.2 

175 

176 

177 

6717.4 

6877.2 
7040.0 

9132.8 

9350-0 
9571.3 

129.91 

264.5 

270.8 
277.2 

8.839 
9.049 
9.263 

347-° 

348.8 

35°-6 

210 

211 

212 

14324.8 
14611.^ 
14902.2 

19475-4 
19864.9 
20260.5 

277.01 
282.58 
288.21 

564.1 

18.848 
19.226 
19.608 

410.0 

411.8 
413.6 

178 

7205.7 

9796.6 

1  39-3  5 

*JS    *J-> 

283.7 

9.481 

352-4 

213 

i5r97-5 

20661.9 

293.92 

598.3 

19.997 

4I5-4 

179 

7374-5 

10026.1 

142.62 

290.3 

9-703 

354-2 

214 

15497.2 

21069.3 

299.72 

610.2 

20.391 

417.2 

180 

181 
182 

7546.; 
7899. 

10259.7 
10497.7 
10739.9 

H5-93 

149.32 

r52-77 

297.1 
304.0 
311.0 

9.929 

10.150 
10.394 

357-8 
359-6 

215 

216 

217 

15801.3 
16109.9 
16423.2 

21482.8 
21902.4 
22328.3 

305.57 

3"-57 
317.62 

622.1 
634-2 
646.6 

20.791 
21.197 
21.690 

4190 

420.8 
422.6 

183 

8080.8 

10986.4 

318.1 

10.633 

361.4 

218 

16740.9 

22760.' 

323.78 

22.027 

424.4 

I& 

8265.4 

11237.3 

159.84 

325-4 

10.876 

363-2 

219 

17063.3 

23198.6 

330-01 

671.8 

22.452 

426.2 

185 

1  86 
187 

8453.2 
8644.4 
8838.8 

11490.0 

11752-5 
12016.9 

163.47 
167.17 
170.94 

332.3 
340.3 
348.0 

11.123 

n-374 
11.630 

365-0 

366.8 
368.6 

220 

22 

22 

17390.4 
17722.1 
18058.6 

23643- 
24094. 

2455I- 

336-3C 

342.70 

349-21 

684.7 

6977 
711.0 

22.882 

23-319 
23.761 

4280 

429.8 
431.6 

1  88 
189 

/- 
9036.7 

9238.0 

12285.9 
12559.6 

174.76 
178.6 

355-8 
363- 

u.88 
12.15 

370-4 
372- 

22 

22; 

18399.9 
18746.1 

25015. 
25486. 

355-8i 
362-5C 

724.4 
738.0 

24.210 
24.666 

433-4 
435-2 

190 

19 
192 

193 

194 

9442.7 
9650.9 
9862. 
10078.0 
10297.0 

12837-9 
13121.0 
13408.9 
13701.7 
13999-4 

182.6 
186.63 
190.7 
194.88 
199.1 

38ac 
388. 
396.8 
405-4 

12.42 
12.69 
12.97 
13.26 
13-54 

374-o 

375- 
377- 
379- 
381. 

225 

22 
22 
22 

22 

19097.0 
19452.9 
19813.8 
20179.6 
20550.5 

25963. 
26447. 
26938. 
27435- 
27939- 

369.29 
376.17 

383-if 
390-2: 
397-4C 

$3 

780.9 

794- 
809.0 

25-128 
25-596 
26.07  ! 
26.552 
27.040 

437-0 

438.8 
440.6 
442.4 
444-2 

SMITHSONIAN  TABLES. 


153 


TABLE  166. 

PRESSURE    OF   AQUEOUS   VAPOR,   ACCORDING   TO    BROCH.* 


)  Temp. 

1  -c. 

0.0 

0.2 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

—28 

0.46 

0-45 

o-44 

0-43 

o-43 

0.42 

0.41 

0.40 

0.40 

o-39 

—26 

0.55 

0-54 

0-53 

0.52 

0.51 

0.50 

0.50 

0.49 

0.48 

0.47 

24 

0.66 

0.65 

0.64 

0.63 

0.62 

O.DI 

0.60 

0.58 

o-57 

0.56 

0.79 

0.78 

0.77 

0-75 

o-74 

0.73 

0.71 

0.70 

0.69 

0.68 

—  20 

0.94 

o-93 

0.91 

0.90 

0.88 

0.87 

0.85 

0.84 

0.82 

0.8  1 

—18 

1.  12 

I.IO 

i.  08 

1.  06 

1.05 

1.03 

I.OI 

0.99 

0.98 

0.96 

—  16 

1.32 

1.30 

1.28 

1.26 

1.24 

1.22 

i.  20 

1.18 

1.16 

1.14 

—14 

—  12 

I.56 
1.84 

1.54 

1.81 

l'S78 

1.49 

1-75 

1.46 

1.72 

1.44 
1.69 

1.42 
1.67 

1.64 

'•37 
1.61 

i-35 

T-59 

—  IO 

2.15 

2.12 

2.08 

2.05 

2.02 

1-99 

1.96 

i-93 

1.90 

—8 

2.51 

2.48 

2.44 

2.40 

2.36 

2-33 

2.29 

2.26 

2.22 

2.19 

—6 

2-93 

2.89 

2.84 

2.80 

2.76 

2.72 

2.67 

2.63 

2-59 

2-55 

—  4 

34' 

3.36 

3-31 

3-26 

3.21 

3.16 

3-" 

3-07 

3-03 

2.98 

—  2 

3-95 

3-89 

3-84 

3-78 

3-72 

3-67 

3.62 

3-56 

3-51 

3-46 

—  O 

4-57 

4-50 

4-44 

4-37 

4-31 

4.25 

4.19 

4-13 

4.07 

4.01 

+0 

4-57 

4.64 

4.70 

4-77 

4.84 

4.91 

4-98 

5-°5 

5.12 

5-20 

2 

4 

5-27 
6.07 

5-35 
6.15 

5-42 
6.24 

5-50 
6-33 

5.58 
6.42 

5-66 
6.51 

5-74 
6.60 

5-82 
6.69 

5-90 
6.78 

5-99 
6.88 

6 

6-97 

7.07 

7.17 

7.26 

7.36 

7-47 

7-57 

7.67 

7.78 

7.88 

8 

7-99 

8.10 

8.21 

8.32 

8.43 

8-55 

8.66 

8.78 

8.90 

9.02 

10 

9.14 

9.26 

9-39 

9-51 

9.64 

9-77 

9.90 

10.03 

10.16 

10.30 

12 

10.43 

10.57 

10.71 

20.85 

10.99 

11.14 

11.28 

"•43 

11.58 

H-73 

14 

n.88 

12.04 

12.19 

I2-35 

12.51 

12.67 

12.84 

13.00 

13.17 

16 

13.51 

13.68 

13.86 

14.04 

14.21 

14.40 

14.58 

14.76 

M-95 

15.14 

18 

15-33 

J5-52 

15-72 

15.92 

16.12 

16.32 

16.52 

16.73 

16.94 

20 

17-36 

17-58 

17.80 

18.02 

18.24 

18.47 

18.69 

18.92 

19.16 

'9-39 

22 

19.63 

19.87 

20.  1  1 

20.36 

20.61 

20.86 

21.  II 

21-37 

21.63 

21.89 

24 

22.15 

22.42 

22.69 

22.96 

23.24 

23-52 

23.80 

24.08 

24-37 

24.66 

26 

24.96 

25-25 

25-55 

25.86 

26.16 

26.47 

26.78 

27.10 

27.42 

27.74 

28 

28.07 

28.39 

28.73 

29.06 

29.40 

29-74 

30.09 

30-44 

30.79 

30 

3i.5I 

31-87 

32-24 

32.61 

32.99 

33-37 

33-75 

34-M 

34-53 

34-92 

32 

35-32 
39-52 

35-72 
39-97 

36-13 
40.41 

36.54 
40.87 

36-95 
41.32 

37-37 
41.78 

37-79 

42.25 

38.22 
42.72 

38.65 
43-  T  9 

39.08 
43-67 

36 

44.16 

44-65 

45-J4 

45-64 

46.14 

46-65 

47.16 

47.68 

48.20 

48.73 

38 

49.26 

49-80 

50-34 

50-89 

5*44 

52.00 

52.56 

53-  T  3 

53-70 

54.23 

40 

42 

54-87 
61.02 

55-46 
61.66 

56.05 
62.32 

56-65 
62.98 

57-26 
63-64 

57.87 
64.31 

58-49 
64.99 

59-11 
65.67 

59-74 
66.36 

60.38 
67-05 

44 

67.76 

68.47 

69.18 

69.90 

70.63 

71.36 

72.10 

72.85 

73-6o 

74-36 

46 
48 

75-13 
83.19 

75-91 
84-03 

76.69 
84.89 

77-47 
85-75 

78.27 
86.61 

79.07 
87.49 

79.88 
88.37 

80.70 
89.26 

81.52 
90.16 

82.35 
91.06 

50 

91.98 

92.90 

93-83 

94-77 

95-7i 

96.66 

97-63 

98.60 

99-57 

100.56 

52 

101-55 

102.56 

103-57 

104.59 

105.62 

106.65 

107.70 

108.76 

109.82 

110.89 

54 
56 

111.97 
123.29 

113.06 
124.48 

114.16 
125.67 

115.27 
126.87 

116.39 
128.09 

117.52 
129.31 

118.65 
I30-54 

119.80 

120.95 
I33-04 

122.12 

I34.30 

58 

I35-58 

136.86 

138.15 

139.46 

140.77 

142.10 

143-43 

144.78 

146.14 

60 

62 

148.88 

150.27 
164.79 

151.68 
166.31 

I53-09 
167.83 

J69-37 

1  55-95 
170.92 

157.39 
172.49 

158-85 
174.06 

160.32 

I75-65 

161.80 
177.25 

64 

178.86 

180.48 

182.12 

183-77 

!8543 

187.10 

188.79 

190.49 

192.20 

193.93 

66 

I95-67 

197.42 

199.18 

200.96 

202.75 

204.56 

206.38 

208.21 

210.06 

211.92 

68 

213-79 

215.68 

217.58 

219.50 

221.43 

223.37 

225-33 

227.30 

229.29 

231.29 

*  This  table  is  based  on  Regnault's  experiments,  the  numbers  being  taken  from  Broch"s  reduction  of  the  obser- 
vations (Trav.  et  Mem.  du  Bur.  Int.  des  Poids  et  Mes.  torn.  i).  The  numbers  differ  very  slightly  from  those  of 
Regnault  (see  Table  165).  The  direct  measurements  of  Marvin  given  in  Table  169  show  that  the  numbers  in  this 
table  are  high  for  temperature  below  zero  centigrade. 

SMITHSONIAN   TABLES. 

154 


TABLE  166, 
ESSURE    OF   AQUEOUS   VAPOR,   ACCORDING   TO   BROCH. 


Temp. 

o.o 

0.2 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

70 

72 
74 
76 
78 

233-31 
254-30 
276.87 
301.09 
327-05 

235-34 
256.49 
279.21 
303.60 
329-75 

237-39 
258.69 
281.58 
306.14 
33247 

239-45 
260.91 

283-95 
308.69 
335-20 

241.52 
263.14 
286.35 
311.26 
337-95 

243.62 
265.38 
288.76 
313-85 
340.73 

245-72 
267.65 
291.19 

316-45 
343-52 

247-85 
269.93 
293.64 
319-07 
346.33 

249.98 
272.23 
296.11 
321.72 
349.16 

252.14 

274-54 
298.59 
324-38 
352-01 

80 

82 

84 
86 

88 

354.87 

384.64 
416.47 

450-47 
486.76 

357-76 
387.73 
4I9-77 
454-00 
490.52 

360.67 
390.84 
423.09 
457-54 
494-31 

363-59 
393-97 
426.44 
461.11 
498.12 

366.54 
397-12 
429:81 
464-71 
50L95 

369-51 
400.29 

433-19 
468.32 

505-81 

372.49 
403.49 
436.60 
471.96 
509.69 

375-50 
406.70 
440.04 

475-63 
513-60 

378.53 
409.94 

443-49 
479-32 
5I7-53 

381.58 
4I3-19 
446.97 
483-03 
521.48 

90 

92 

525-47 

566.71 

529.48 
570.98 

533-51 
575.28 

537-57 
579-6i 

§1.65 
3.96 

545-77 
588.33 

549.90 
592.74 

554-07 
597-17 

601.64 

56247 

94 
96 
98 

610.64 

657-40 
707-13 

662.'23 
712.27 

619.76 
667.10 
7  J  7-44 

624.37 
672.00 
722.65 

9.00 
676.00 
727.89 

633.66 
681.88 
733-16 

73846 

643.06 
691.89 
743-80 

647.81 
696.93 
749-  i  7 

652.59 
702.02 

754-57 

100 

760.00 

765-47 

770.97 

776.50 

782.07 

787-67 

- 

- 

- 

- 

TABLE  167. 

WEIGHT    IN    GRAINS   OF  THE    AQUEOUS  VAPOR   CONTAINED  IN  A  CUBIC 
FOOT   OF   SATURATED    AIR.* 


Temp. 

°F. 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

7.0 

80 

9.0 

—10 

0-356 

0.340 

0.324 

0.309 

0.294 

0.280 

0.267 

0.254 

0.242 

0.230 

—  o 

0.564 

0.540 

0.516 

0-493 

0.471 

0.450 

0.430 

0.411 

0.391 

0-373 

H-o 

0.564 

0.590 

0.617 

0.645 

0.674 

0.705 

0-735 

0.767 

0.801 

0.837 

10 

0.873 

0.910 

0.950 

0.991 

1-033 

1.077 

1.  122 

1.169 

I.2I7 

1.268 

20 

1.321 

1-374 

i-43° 

1.488 

I-S49 

i.oii 

1-675 

J-743 

1.812 

1.882 

30 

1.956 

2.034 

2.113 

2.194 

2.279 

2.366 

2-457 

2.55° 

2.646 

2.746 

40 

2.849 

2.955 

3-064 

3-J77 

3-294 

3-4I4 

3-539 

3.667 

3.800 

3-936 

50 

4.076 

4.222 

4-372 

4-526 

4.685 

4.849 

5.016 

5-I9I 

5-370 

5-555 

60 

5-745 

5-941 

6.142 

6-349 

6-563 

6.782 

7.009 

7.241 

7.480 

7.726 

70 

7.980 

8.240 

8.508 

8.782 

9.066 

9-356 

9-655 

9.962 

10.277 

10.601 

80 

10.934 

11.275 

11.626 

11.987 

12.356 

12.736 

13.127 

13.526 

1  3-937 

1  4-359 

90 

14.790 

I5-234 

15.689 

16.155 

16.634 

17.124 

17.626 

18.142 

18.671 

19.212 

100 

IIO 

19.766 
26.112 

26.832 

20.917 
27.570 

21.514 
28.325 

22.125 
29.096 

22.750 
29.887 

23-392 

24.048 

24.720 

25408 

TABLE  168. 

WEIGHT    IN    GRAMMES    OF    THE    AQUEOUS    VAPOR    CONTAINED    IN    A 
CUBIC    METRE    OF    SATURATED    AIR. 


Temp. 
C. 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

70 

8.0 

9.0 

—20 

1.078 

0.992 

0.913 

0.839 

0.770 

0.706 

0.647 

0-593 

0.542 

0.496 

—  10 

2.363 

2.192 

2.032 

1.882 

1.742 

1.611 

1.489 

1-375 

1.269 

1.170 

—  o 

4.835 

4-513 

4.211 

3-926 

3-659 

3-407 

3-I7I 

2-949 

2.741 

2.546 

+0 

4.835 

5-J76 

5.538 

5.922 

6.330 

6.761 

7-219 

7-703 

8.215 

8-757 

IO 

20 

9-33° 
17.118 

9-935 
18.143 

10.574 
19.222 

11.249 

20-355 

11.961 
21.546 

12.712 
22.796 

13-505 
24.109 

14-339 

25.487 

15.218 
26.933 

16.144 
28.450 

30 

30.039 

31-704 

33-449 

35-275 

37-I87 

39-i87 

41.279 

43-465 

45-751 

48.138 

SMITHSONIAN  TABLES. 


*  See  "  Smithsonian  Meteorological  Tables,"  pp.  132-133. 
155 


TABLE  169. 

PRESSURE    OF   AQUEOUS   VAPOR   AT    LOW   TEMPERATURE.* 

Pressures  are  given  in  inches  and  millimetres  of  mercury,  temperatures  in  degrees  Fahrenheit  and  degrees  Centigrade. 


(a)  Pressures  in  inches  of  mercury  ;  temperatures  in  degrees  Fahrenheit. 

Temp.  F. 

o°.o 

l«.p 

2°.0 

3°.0 

*».o 

6°.0 

6°.0 

7°.0 

8°.0 

9°.0 

—50° 

OOO2I 

0.0019 

0.0018 

0.0017 

0.0016 

0.0015 

0.0013 

0.0013 

0.0012 

0.00  1  1 

—40 

.0  :>}9 

.0037 

•0035 

•0033 

•0031 

.0029 

.0027 

.0026 

.OO24 

.0022 

—30 

20 

.0  6) 
-OI  :::> 

.0065 
.01  19 

.0061 
.0112 

•0057 
.0106 

.0054 
.0100 

.0051 
.0094 

.0048 
.0089 

.0046 
.0083 

.0044 
.0078 

.OO4I 
.0074 

IO 

.0222 

.0210 

.0199 

.0188 

.0178 

.0168 

.0159 

•0150 

.0141 

•0133 

—0 

0.0383 

0.0263 

0.0244 

0.0225 

0.0307 

0.0291 

0-0275 

0.0260 

O.O247 

0.0234 

~f~° 

•0383 

.0403 

•0423 

•0444 

.0467 

.0491 

•0515 

.0542 

.0570 

.0600 

IO 

.0665 

.0699 

•0735 

.0772 

.0810 

.0850 

.0891 

•0933 

.0979 

20 

.1026 

.1077 

.1130 

.1185 

.1242 

.1302 

.1365 

.1430 

.1497 

.1568 

30 

.1641 

.1718 

.1798 

(V)  Pressures  in  millimetres  of  mercury  ;  temperatures  in  degrees  Fahrenheit. 

Temp.  F. 

o°.o 

10.0 

2°.0 

3°.0 

4°.0 

5°.0 

6°.0 

7°.0 

8°.0 

9°.0 

—50° 

0-053 

0.049 

0.046 

0.043 

0.040 

0.037 

0.034 

0.032 

0.030 

0.028 

—40 

.100 

•094 

.089 

.084 

.079 

.074 

.069 

.065 

.061 

-057 

—3° 

.176 

.I65 

.155 

.146 

.138 

.130 

.123 

.117 

.in 

.105 

—  20 

•3J9 

.301 

.284 

.268 

•253 

•239 

.225 

.212 

.199 

.187 

—  10 

.564 

•534 

•505 

.478 

•452 

•427 

.403 

.384 

•358 

.338 

—0° 

0.972 

0.922 

0.873 

0.826 

0.781 

0.738 

0.698 

0.661 

0.627 

0-595 

~f~o 

•972 

1.023 

1.075 

1.129 

1.186 

1.246 

1.309 

1.376 

1.447 

10 

20 

1.603 
2.607 

1.688 
2-735 

1.776 
2.869 

1.867 
3.009 

1.961 

2.058 
3-3°7 

2.158 
3.466 

2.262 
3-63I 

2.371 
3-803 

2.486 
3-982 

30 

4.169 

4-364 

4.568 

(C)  Pressures  in  inches  of  mercury  ;  temperatures  in  degrees  Centigrade. 

Temp.  C. 

o°.o 

lo.O 

2°.0 

3°.0 

4°.0 

5°.0 

6°.0 

7°.0 

8°.0 

9°.0 

—0° 

0.1798 

0-1655 

0-1524 

0-1395 

0.1290 

0.1185 

0.1091 

0.0998 

0.0916 

0.0842 

—  10 

.0772 

.0706 

.0645 

.0588 

•0537 

.0491 

.0449 

.0411 

•°375 

.0341 

—  20 

.0307 

.0278 

.0252 

.0229 

.0208 

.0188 

.0171 

•0153 

.0138 

.0124 

—30 

.0112 

.0101 

.0091 

.0082 

.0073 

.0065 

-0059 

•°°53 

.0048 

.0044 

—40 

.0040 

.0036 

.0032 

.0029 

.0025 

.0022 

.0020 

.0017 

.0015 

.0013 

(d)  Pressures  in  millimetres  of  mercury  ;  temperatures  in  degrees  Centigrade. 

Temp.  C. 

o°.o 

1*« 

2°.0 

3°.0 

4°.0 

5°.0 

6°.0 

7°.0 

8°.0 

9°.0 

—0° 

4.568 

4.208 

3-875 

3-565 

3-277 

3-009 

2.767 

2-534 

2.327 

2.138 

—  10 

1.961 

1.794 

1.637 

1-493 

I-363 

1.246 

1.140 

1.044 

0.952 

0.864 

—  20 
—30 

0.781 
0.284 

0.706 
0.256 

0.641 
0.231 

0-583 
0.207 

0.528 
0.185 

0.478 
0.165 

0.432 
0.148 

0.389 
0-133 

0-350 

O.I  21 

o-3  1  5 

O.IIO 

—40 

O.I  00 

0.090 

0.081 

0.072 

0.064 

0.057 

0.050 

0.044 

0.039 

0.034 

*  Marvin's  results  (Ann.  Kept.  U.  S.  Chief  Signal  Officer,  1891,  App.  10). 
SMITHSONIAN  TABLES. 


156 


TABLE   1  7O. 
PRESSURE    OF   AQUEOUS   VAPOR    IN    THE    ATMOSPHERE. 

This  table  gives  the  vapor  pressure  corresponding  to  various  values  of  the  difference  t  —  ^  between  the  readings  of 
dry  and  wet  bulb  thermometers  and  the  temperature  /t  of  the  wet  bulb  thermometer.  The  differences  t  — 1±  are 
given  by  two-degree  steps  in  the  top  line,  and  ^  by  degrees  in  the  first  column.  Temperatures  in  Centigrade 
degrees  and  Regnault's  vapor  pressures  in  millimetres  of  mercury  are  used  throughout  the  table.  The  table  was 
calculated  for  barometric  pressure  B  equal  to  76  centimetres,  and  a  correction  is  given  for  each  centimetre  at  the 
top  of  the  columns.* 


«, 

'£* 

2 

4 

6 

8 

10 

12 

i* 

16 

18 

20 

Difference  per  1 
*°off-ft 

Corrections  for 
B  per  centi- 
metre. t 

.013 

.026 

.040 

•053 

.066 

.079 

.092 

.106 

.119 

•  132 

—10 

i.96 

0.96 

O.IOO 

—9 

2.14 

1.14 

0.14 

O.IOO 

—8 

2-33 

J-33 

P-33 

O.IOO 

—7 

2-53 

'•53 

o-53 

Example. 

O.IOO 

—6 

1.76 

0.76 

t  —  tl=   7.2 

O.IOO 

—5 

3.01 

2.01 

I.OO 

/I  —  IO.O 

O.IOO 

—4 

3-28 

2.28 

1.27 

0.27 

-#  —  74-5 
Tabular  number  =  6.  12  —  6X.ioi=:   5.51 

O.IOO 

—3 

3-57 
3-88 

l'& 

1.56 
1.87 

0.56 
.  0.87 

Correction  for  Z?—  1.5  X  .048  .  .  —     .07 
Hence  we  get/  .  .  .  =   5.58 

O.IOO 
O.IOO 

—i 

4.22 

3-22 

2.21 

1.  21 

0.21 

O.IOO 

0 

4.60 

3.60 

2-59 

i-59 

o-59 

O.IOO 

i 

4.94 

3-93 

2.92 

1.92 

0.92 

O.IOO 

2 

5-3° 

4.29 

3-29 

2.28 

1.28 

0.27 

O.IOO 

3 

5.69 

4-68 

3-68 

2.67 

1.66 

0.66 

O.IOI 

4 

6.10 

5-09 

4.09 

3.08 

2.07 

1.  06 

0.05 

O.IOI 

5 

6-53 

5-52 

4-5' 

3-50 

2.49 

1.48 

0.48 

O.IOI 

6 

7.00 

5-99 

4.98 

3-97 

2.96 

!-95 

0.94 

O.IOI 

7 

7-49 

6.48 

547 

445 

344 

243 

1.42 

0.41 

O.IOI 

8 

8.02 

7.01 

5-99 

4.98 

3-97 

2.96 

1.94 

0.93 

O.IOI 

9 

8-57 

7-56 

6-54 

5-53 

4-5' 

3-5° 

2.49 

1.48 

0.46 

O.IOI 

10 

9.17 

8.16 

7.14 

6.12 

5-11 

4-09 

3.08 

2.07 

1.  06 

0.05 

O.IOI 

ii 

9-79 

8.77 

7.76 

6.74 

5-73 

4.71 

3-69 

2.68 

1.66 

0.64 

O  IO2 

12 

10.46 

9-44 

843 

7.41 

6-39 

5-37 

4-36 

3-34 

2.32 

1.30 

0.28 

O.I  O2 

13 

n.  16 

10.14 

9.12 

8.10 

7.09 

6.07 

5-°5 

4-03 

3-oi 

1.99 

0.97 

O.I  O2 

14 

11.91 

10.89 

9.87 

8.85 

7-83 

'   6.8  1 

5-79 

4-77 

2.69 

l.67 

O.I  O2 

15 

12.70 

11.68 

10.66 

9-64 

8.62 

7.60 

6.58 

5.56 

4-54 

3-52 

2.50 

O.I  O2 

16 

13-54 

12.52 

11.50 

10.47 

9-45 

8-43 

7.41 

6-39 

5-37 

4-35 

3-33 

0.102 

J7 

14.42 

13.40 

12.37 

"•35 

10.33 

9.31 

8.28 

7.26 

6.24 

5-22 

4.20 

O.IO2 

18 
19 

I5-36 
16.35 

14-34 
15-33 

'3-31 
14.30 

12.29 
13.27 

11.26 

12.25 

10.24 

11.22 

9.21 

IO.2O 

8.19 

9.17 

7.17 
8.15 

6.15 
7-13 

6.  1  1 

O.I  O2 
O.I  O2 

20 

'7-39 

16.37 

!5-34 

I4-31 

13.28 

12.26 

11.23 

10.21 

9.18 

8.15 

7.12 

0103 

21 

18.50 

1747 

16.45 

15.42 

1439 

I3-36 

12-33 

11.31 

10.28 

9-25 

8.22 

0.103 

!       22 

19.66 

18.63 

17.60 

16.57 

J5-54 

13.48 

12.46 

"43 

10.40 

9-37 

0.103 

23 

24 

20.89 
22.18 

19.86 
21-15 

18.83 

20.  1  2 

17.80 
19.09 

16.77 
18.05 

15-74 
17.02 

1471 
15.99 

13.68 
14.96 

12.66 
13-94 

11.63 
12.91 

1  0.60 
11.88 

0.103 
0.103 

25 

26 

23-55 
24.99 
26.51 
28.10 

22.52 
23.96 
25.48 

27.07 

21.49 
22.92 

24.44 
26.03 

20.45 
21.89 
23.40 
24.99 

19-43 
20.86 

22.37 
23.96 

18.39 
19.82 
21-34 

22.92 

I7-36 
18.79 
20.30 
21.89 

16.33 
17.76 
19.27 
20.85 

15-30 
16.73 
18.24 
19.82 

14.27 
15-70 
17.21 
18.79 

13.24 
14.67 
16.18 
17.76 

0.103 

0.103 
0.103 
0.103 

29 

29.78 

28.75 

2771 

26.67 

25-63 

24-59 

23-56 

22.52 

21.49 

20.46 

1943 

0.103 

30 

31 

32 
33 
34 

3'-55 
33-41 
35-36 
3741 
39-57 

30-51 

32-37 
34-32 
36.37 
38.53 

29.47 

31-33 

33-28 

35-33 
37.48 

28.43 
30.29 
32.24 
34-29 
3644 

27.40 
:  29.25 
31.21 

33-25 
3540 

26.36 
28.22 
30.17 
32.22 

I*?! 

29.13 
3I.I8 
33-32 

24.29 
26.14 
28.09 
30.14 
32.28 

23-25 
25.10 
27.05 
29.10 
31.24 

22.22 
24.07 
26.01 
28.06 
3O.2O 

21.  18 

23-03 
2497 
27.02 
29.16 

o  104 

0.104 
0.104 
0.104 
0.104 

35 

36 

39 

41.83 
44.20 
46.69 

49-3° 
52.04 

40.79 
43-<6 

45-65 
48.26 
51.00 

39-74 
42.11 
44.60 
47.21 
49-95 

38.70 
41.07 
43-56 
46.17 
48.91 

37-66 
40.03 
42.52 

45-  !  3 
47.86 

36.62 
38.99 

4r.48 
44.08 
46.82 

35-68 

37-95 
40.44 

43-°4 
45-77 

36.90 

39-39 
41.99 

44-73 

33-60 
35.86 

38-35 
40.95 
43.78 

32.56 
34.82 

37-3^ 

39-91 
42.74 

33-78 
36-27 
38-87 
41.69 

0.104 
c.i  04 
0.104 
0.104 
0.105 

i 

*  The  tahle   was  calculated  from  the  formula  /=A  -  0.00066  £  (t -(,)  (i  +0.00115  A)  (Ferrel,  Annual  Report 
U'  t' When  ^Tr/eS^han  ^The^Trrection  is  to  be  added,  and  when  B  is  greater  than  76  it  is  to  be  subtracted. 
SMITHSONIAN  TABLES. 

!57 


TABLE  171. 


DEW- 


The  first  column  of  this  table  gives  the  temperatures  of  the  wet-bulb  thermometer,  and  the  top  line  the  difference 
the  table.  The  dew-points  were  computed  for  a  barometric  pressure  of  76  centimetres.  When  the  barometer  differs 
and  the  resulting  number  added  to  or  subtracted  from  the  tabular  number  according  as  the  barometer  is  below  or 


I 

,-*=! 

2 

3 

4 

5 

6 

7 

8 

Dew-points  corresponding  to  the  difference   of  temperature  given  in  the  above  line  and  the 
wet-bulb  thermometer  reading  given  in  first  column. 

87755  = 

.04 

.11 

.22 

49 

—  10 

—  13.2 

—  17.9 

—  9 

I2.O 

16.0 

—  22.0 

—  8 

10-7 

14-3 

194 

—  7 

9-5 

12.7 

I7.I 

—  24.0 

—  6 

8-3 

II.  2 

14.9 

20.3 

S  7/5  5  = 

.03 

.06 

.11 

.18 

.31 

43 

—  5 

—  7-1 

—  9-7 

—  12.9 

—  17-5 

—  24-5 

—  4 

6.0 

8-3 

II.  I 

14.8 

20.1 

—  3 

4.8 

6.9 

94 

12.6 

1  6.8 

—  234 

2 

3-6 

5-5 

7-8 

10.5 

13-9 

18.9 

—  I 

2-5 

4.2 

6.2 

8.5 

11.5 

154 

—  2I.O 

57/85  = 

.02 

.04 

.07 

.10 

.14 

.19 

.26 

•38 

0 

—  1-3 

—  2.9 

-4-8 

—  6.8 

—  9-3 

—  12.3 

-I6.5 

—  22.9 

i 

o-3 

1.7 

3-5 

5-3 

7.6 

10.2 

18.3 

2 

+  0.6 

0.7 

2.2 

3-9 

6.1 

8-3 

II.  I 

14.7 

3 

1.7 

+  0.2 

1.0 

2.6 

4.6 

6.4 

8.9 

11.9 

4 

2.8 

1.4 

o.o 

1.3 

3-1 

4-7 

6.9 

94 

87/55  = 

.02 

•03 

05 

.07 

.09 

.11 

.14 

.18 

5 

3-8 

2.6 

+  1.2 

—  O.I 

—  1.6 

—  3-2 

—  7.1 

6 

4-9 

.  3-7 

2-5 

+  I-1 

O.2 

3-3 

5-2 

7 

6.0 

4.9 

3-7 

2.4 

+  J'1 

o-3 

1.8 

34 

8 

7.0 

6.0 

4.9 

3-7 

2-5 

+  1.1 

0.3 

1.8 

9 

8.1 

7-r 

6.1 

5.0 

3-9 

2.6 

+  1.2 

O.I 

87/55  = 

.01 

.02 

.03 

05 

.06 

.08 

.IO 

.12 

10 

9.1 

8-3 

7-3 

6-3 

S-2 

4.1 

2.8 

+  1.5 

ii 

12 

10.2 
II.  2 

9-3 
10.4 

8.4 
9.6 

87 

5 

U 

4-3 
5-8 

4-7 

13 

12.3 

»-S 

10.7 

9.9 

9.1 

8.2 

7-2 

6.2 

87/55  = 

13-3 
.01 

12.6 
.02 

11.9 
•03 

n.  i 
.04 

10.3 
.05 

9.0  s 
.06 

8.6 
.07 

7.6 
.08 

15 

14.4 

13.7 

13.0 

12.3 

10.8 

9.9 

9.1 

16 

154 

I4.8 

14.1 

12.7 

12.0 

n-3 

10.5 

'7 

I6.4 

15.8 

'5-2 

14.6 

13-9 

13-3 

12.6 

1  1.8 

18 

*fS 

16.9 

16.3 

I5-7 

14-5 

13.8 

13.1 

19 

18.5 

18.0 

17.4 

16.9 

16.3 

IS-7 

14.4 

5  7/55  = 

005 

.01 

.015 

.02 

.027 

•033 

.04 

20 

19-5 

19.0 

18.5 

1  8.0 

17.4 

16.9 

16.3 

J5-7 

21 

20.5 

20.  i 

19.6 

19.1 

1  8.6 

18.1 

17.0 

22 

21.6 

21.  1 

20.7 

20.2 

19.7 

19.2 

ls.7 

18.2 

23 

22.6 

22.2 

21.7 

21.3 

20.8 

20.4 

19.9 

19.4 

24 

23.6 

23.2 

22.8 

22.4 

22.0 

21.5 

21.  1 

20.6 

8  7/55  = 

.005 

.OI 

.015 

.02 

.025 

•03 

•035 

.04 

25 

24.6 

24.2 

23-9 

23-5 

23.1 

22.7 

22.2 

21.8 

26 

25.6 

25-3 

24.9 

24.2 

23.8 

234 

23.0 

27 
28 

27.7 

26.3 

27-3 

26.0 

27.0 

25.6 
26.7 

26.4 

24.9 
26.0 

24-5 
25-7 

24.1 

25-3 

29 

28.7 

28.4 

28.1 

27-8 

274 

27.1 

26.8 

y 

26.4 

8  7/55  = 

.003 

.006 

.01 

.013 

.017 

.019 

.022 

.026 

30 

29.7 

29.4 

29.1 

28.8 

28.5 

28.2 

27.9 

27.6 

31 

30.7 

30-5 

30.2 

29.9 

29.6 

29-3 

29.0 

28.7 

32 

3'-7 

31.5 

31.2 

30-9 

30-7 

304 

3O.I 

29.8 

33 

32-8 

32.5 

32.2 

32.0 

31-7 

31.2 

3°-9 

34 

33-8 

33-5 

33-3 

32.8 

32.5 

32-3 

32.0 

5  7/55  = 

003 

005 

.008 

.OIO 

.013 

.016 

.021 

35 

34-8 

34-5 

34-3 

34-i 

33-8 

33-6 

334 

33.1 

36 

35-8 

35-5 

35-3 

34-9 

34-6 

344 

34-2 

3l 

36.8 

366 

364 

36.2 

36.0 

35-7 

35-3 

38 

37-8 

37-6 

374 

37-2 

37-o 

36.8 

36  6 

364 

39 

38.8 

38.6 

384 

38.2 

38.0 

37-9 

37^6 

37-5 

SMITHSONIAN  TABLES. 


158 


POINTS. 


TABLE  171. 


between  the  dry  and  the  wet  bulb,  when  the  dew-point  has  the  values  given  at  corresponding  points  in  the  body  of 
from  76  centimetres  the  corresponding  numbers  in  the  lines  marked  &T/&£  are  to  be  multiplied  by  the  difference, 
or  above  76.  See  examples. 


* 

«-,,  =  . 

10 

11 

12 

13 

14 

15 

Dew-points  corresponding  to  the  difference  of  temperature  given  in  the  above  line  and  the 
wet-bulb  thermometer  reading  given  in  first  column. 

EXAMPLES. 

(i)  Given  £=72,  ti=io,  *•—  ^=5. 

Then  tabular  number  for  t,=  10  and  t  —  t\  —  S  is  5.2 
Also  76  —  72  =  4  and  B7'/SB=.o6. 
'   Correction  —  o  06  X  4~""*                 .                 •       .24 

(2)  Given  £  =  71.5,  t^  =  7,  /  —  /t  =  8. 
Then,  as  above,  tabulated  number  =        .        .     3.4 

2 

8773^  = 

•45 

.67 

J-'c"    1 

0 

2 

—  2O.O 

3 

I5.8 

—  22.2 

4 

12.4 

1  6.8 

s  zys/?  = 

23 

.29 

•37 

•  '.44 

•54 

.66 

•72 

5 

—  19.8 

—  13.1 

—  17.7 

6 

74 

IO.I 

134 

—  18.1 

7 

5-3 

7.6 

IO.I 

13-5 

-18.3 

8 

3-3 

5-2 

74 

IO.I 

I3-S 

-18.3 

9 

1.6 

3-2 

5-1 

7.2 

9-9 

I3>1 

-17.2 

5  T/W  — 

.14 

.20 

.22 

25 

•29 

•36 

10 

0.0 

—  1.3 

—  3-° 

—  4-7 

—  6.8 

—  94 

—  12.5 

ii 

+  1.8 

+  0.3 

I.O 

2.6 

4-3 

6-3 

8.8 

12 

3-5 

2.2 

+  0.8 

0.6 

2.1 

3-7 

5-7 

13 

3-9 

2.7 

+  1.3 

O.I 

1.6 

3-i 

H 

6.7 

5.6 

4-5 

3-3 

+  1.9 

+  0.5 

0.9 

5  T/W  = 

.09 

.11 

.12 

.14 

.16 

.18 

.20 

15 

8.2 

7.2 

6.2 

5-1 

3-9 

2.7 

~H  I>3 

16 

9.6 

8.7 

7.8 

6.8 

5-8 

4-7 

3-5 

II.O 

10.2 

94 

8.5 

7-5 

6.5 

5-5 

18 

12.4 

II.7 

10.9 

IO.I 

0,2 

8-3 

74 

13.8 

13-1 

12.4 

1  1.6 

10.8 

IO.O 

9-;3 

8  T/W  = 
20 

06 

.07 

14-5 

.08 

13-8 

.09 
13-1 

.10 
12.4 

.11 
1  1.6 

108 

21 

16  4 

15.8 

15.2 

14-5 

13-9 

13.2 

12.5 

22 
23 
24 

25 

17.6 
18.9 

20.1 

•045 
21-4 

17.1 

18.4 
19.6 
.05 

20.9 

16.5 
17.9 
19.2 
.06 
20.4 

15-9 
17-3 
18.7 
.06 

2O.O 

\n 

18.1 
.07 
19-5 

14.7 
16.2 
17.6 

.08 

19.0 

14.0 

15-7 
17.0 
.09 
18.5 

26 

22.6 

22.1 

21.7 

21.3 

20.8 

20.3 

19.9 

27 
28 

29 
30 

32 
33 

23-7 
24.9 
26.1 
.031 

27.2 
28.4 
29-5 
30-7 
71.8 

234 

24-5 

25-7 

.035 

26.9 
28.1 
29.2 
304 
3T-5 

22.9 
24.2 
25.4 
.041 
26.6 
27.8 
28.9 
30.1 
31.2 

22.; 
23-8 
25.0 
.047 
26.2 
27.4 
28.6 
29.8 

3°-9 

22.1 
234 
24.6 
•053 
25.9 
27.1 
28.3 
29-5 
30-7 

21.7 
23.0 
24.2 
.06 

HI 

28.0 
29.2 
30.4 

21.2 
22.6 

'*£ 
'£ 

27.7 
28.9 
3O.I 

35 

36 
VI 

o 

.024 

32.9 

34-o 

.027 
32.6 
33-7 
34-9 

.029 

324 
33-5 
34-6 

.032 
32.1 
33-3 
344 

•037 

31.8 

33-° 
34-2 

.037 
31.6 
32.8 
33-9 

.04 
314 

32-5 

Hi 

38 

39 

36.2 
37-3 

35-9 

37-i 

$ 

35-3 
364 

36.2 

34-8 
36.0 

SMITHSONIAN  TABLES. 


159 


TABLE  1  72. 


VALUES   OF   0.378C.* 


This  table  gives  the  humidity  term  0.378  <?,  which  occurs  in  the  equation  S  =  fi0  — -  =  80 °'3?       for  the  calcu- 

700  700 

lation  of  the  density  of  the  dry  air  in  a  sample  containing  aqueous  vapor  at  pressure  e ;  So  is  the  density  at  normal 
barometric  pressure,  B  the  observed  barometric  pressure,  and  h  the  pressure  corrected  for  humidity.     For  values 


of  JL  see  Table  174. 
760 


Temperatures  are  in  degrees  Centigrade,  and  pressures  in  millimetres  of  mercury. 


Dew- 
point. 

Vapor 
pressure. 
e 

0.378  e. 

Dew- 
point. 

Vapor 
pressure. 
e 

0.378  e. 

Dew- 
point. 

Vapor 
pressure. 
e 

0.378  e. 

—  30° 

0.38 

0.14 

0 

4-57 

1-73 

30° 

3I-5I 

11.91 

=  3 

.42 
.46 

.16 
•17 

I 

2 

4.91 

5-27 

1.99 

32 

33-37 
35-32 

12.61 
U-35 

—  27 

•50 

.19 

3 

5.66 

2.14 

33 

37-37 

14-13 

—  26 

•55 

.21 

4 

6.07 

2.29 

34 

39.52 

14.94 

—  25 

—  24 

0.61 
.66 

0.23 

5 

6 

6.51 
6.97 

2.46 
2.63 

35 

36 

41.78 
44.16 

'5-79 
16.69 

—  23 

•73 

.28 

7 

7-47 

2.82 

46.65 

J7-63 

—  22 

•79 

•3° 

8 

7-99 

3.02 

38 

49.26 

18.62 

—  21 

.87 

•33 

9 

8.55 

3-23 

39 

52.00 

19.66 

—  20 

0.94 

0.36 

10 

9.14 

3-45 

40 

54-87 

20.74 

—  19 

1.03 

•39 

ii 

'  -9-77 

3-69 

41 

57-87 

21.86 

—  18 

.12 

.42 

12 

10.43 

3-94 

42 

61.02 

23.06 

—  17 

.22 

.46 

13 

11.14 

4.21 

43 

64.31 

24.31 

—  16 

•32 

•50 

14 

u.88 

4-49 

44 

67.76 

25.61 

—  15 

1-44 

0-54 

15 

12.67 

4-79 

45 

71-36 

26.97 

—  14 

•5J9 

16 

13.51 

5-11 

46 

75-13 

28.40 

—  13 

.69 

.64 

17 

14.40 

5-44 

47 

79.07 

29.89 

—  12 

.84 

.70 

18 

15-33 

5-79 

48 

83.19 

3^-45 

—  II 

•99 

•75 

19 

16.32 

6.17 

49 

87.49 

33-°7 

—  10 

2-I5 

0.81 

20 

17-36 

6.56 

50 

91.98 

3477 

—  9 

•33 

.88 

21 

18.47 

6.98 

51 

96.66 

36-54 

—  7 

•51 
•72 

•95 
1.03 

22 
23 

19.63 
20.86 

7.42 
7.89 

52 
53 

IO'-55 
106.65 

38.39 
40.31 

—  6 

•93 

.11 

24 

22.15 

8-37 

54 

111.97 

42.32 

—  5 

3.16 

1.19 

25 

23-52 

8.89 

55 

117.52 

44.42 

—  4 

.41 

.29 

26 

24.96 

9-43 

56 

123.29 

46.60 

—  3 

.67 

•39 

27 

26.47 

10.01 

57 

129.31 

48.88 

2 

•95 

.49 

28 

28.07 

10.61 

58 

I35-58 

51-25 

—  I 

4-25 

.61 

29 

29.74 

11.24 

59 

142.10 

53-71 

*  This  table  is  quoted  from  "  Smithsonian  Meteorological  Tables,"  p.  225. 
SMITHSONIAN  TABLES. 

160 


TABLE  173. 


RELATIVE    HUMIDITY.* 


This  table  gives  the  humidity  of  the  air,  for  temperature  /  and  dew-point  d  in  Centigrade  degrees,  expressed 
in  percentages  of  the  saturation  value  for  the  temperature  t. 


Depression  of 
the  dew-point. 
t  —  d 

Dew-point  (d). 

Depression  of 
the  dew-point. 
t  —  d 

Dew-point  (d). 

10 

o 

+  10 

+  20 

+  30 

—  10 

o 

+  10 

+  20 

+  30 

C. 

C. 

o°.o 

100 

100 

100 

100 

100 

8°.0 

54 

57 

60 

62 

64 

O.2 

98 

99 

99 

99 

99 

8.2 

54 

56 

59 

61 

0.4 

97 

97 

97 

98 

98 

8.4 

53 

56 

58 

60 

63 

0.6 

95 

96 

96 

96 

97 

8.6 

52 

55 

57 

60 

62 

0.8 

94 

94 

95 

95 

96 

8.8 

54 

57 

59 

61 

1.0 

92 

93 

94 

94 

94 

9.0 

51 

53 

56 

58 

61 

1.2 

92 

92 

93 

93 

9.2 

5° 

53 

55 

58 

60 

1.4 

90 

91 

92 

92 

94 

49 

52 

55 

57 

59 

1.6 

88 

89 

91 

91 

9.6 

48 

51 

54 

56 

59 

1.8 

87 

88 

89 

90 

90 

9.8 

48 

53 

56 

58 

2.0 

86 

87 

88 

88 

89 

10.0 

47 

5° 

53 

55 

57 

2.2 

84 

85 

86 

87 

88 

10.5 

45 

48 

51 

54 

2-4 

83 

84 

85 

86 

87 

n.o 

44 

47 

49 

52 

2.6 

82 

83 

84 

85 

86 

"•5 

42 

45 

48 

2.8 

80 

82 

83 

84 

85 

I2.O 

4i 

44 

47 

49 

3.0 

79 

81 

82 

83 

84 

12.0 

39 

42 

45 

48 

3-2 

78 

80 

81 

82 

83 

13.0 

38 

41 

44 

46 

3-4 

77 

79 

80 

81 

82 

J3-5 

37 

40 

43 

45 

3-6 

76 

77 

79 

80 

82 

14.0 

35 

38 

41 

44 

3-8 

75 

76 

78 

79 

81 

H-5 

34 

37 

40 

43 

4.0 

73 

75 

77 

78 

80 

15.0 

33 

36 

39 

42 

4.2 

44 
4.6 

72 
7i 
70 

74 
73 

72 

76 
75 
74 

77 

M 

7Q 

77 

'5-5 
16.0 
16.5 

32 
30 

35 
34 

33 

1 

40 
38 

4-8 

69 

73 

75 

76 

17.0 

29 

32 

35 

37 

5.0 

68 

70 

72 

74 

75 

17.5 

28 

31 

34 

36 

S-2 

67 

73 

75 

1  8.0 

27 

3° 

33 

35 

54 

66 

68 

70 

72 

74 

18.5 

26 

29 

32 

34 

5.6 

65 

67 

69 

73 

19.0 

25 

28 

31 

33 

5-8 

64 

66 

69 

70 

72 

19-5 

24 

27 

30 

33 

6.0 

63 

66 

68 

70 

71 

20.0 

24 

26 

29 

32 

6.2 

62 

6c 

67 

69 

71 

2I.O 

22 

25 

27 

6.4 

61 

64 

66 

68 

70 

22.O 

21 

23 

26 

6.6 

60 

63 

65 

67 

23.0 

19 

22 

24 

6.8 

60 

62 

64 

66 

68 

24.0 

18 

21 

23 

7.0 

59 

61 

63 

66 

68 

25.0 

17 

JQ 

22 

7.2 

58 

60 

63 

65 

67 

26.0 

16 

18 

21 

74 

57 

60 

62 

64 

66 

27.0 

15 

17 

2O 

7.6 

56 

59 

61 

63 

65 

28.0 

14 

16 

19 

7-8 

55 

58 

60 

63 

65 

29.0 

«3 

15 

18 

8.0 

54 

57 

60 

62 

64 

30.0 

12 

14 

17 

*  Abridged  from  Table  45  of  "  Smithsonian  Meteorological  Tables." 
SMITHSONIAN  TABLES. 

161 


TABLES  174,  175. 

DENSITY  OF  AIR   FOR  DIFFERENT  PRESSURES  AND  HUMIDITIES. 


TABLE  174.  —  Values  oi        ,  from 


=  l  to  h  =  9,  for  the  Computation  of  Different  Values  of  the  Ratio 
of  Actual  to  Normal  Barometric  Pressure. 


This  gives  the  density  of  air  at  pressure  h  in  terms  of  the  density  at  normal  atmosphere  pressure.  When  the  air 
contains  moisture,  as  is  usually  the  case  with  the  atmosphere,  we  have  the  following  equation  for  the  dry  air 
pressure  :  h  —  B  —  0.378*,  where  e  is  the  vapor  pressure,  and  B  the  observed  barometric  pressure  corrected  for 
temperature.  When  the  necessary  observations  are  made  the  value  of  e  may  be  taken  from  Table  170,  and  then 
0.378*  from  Table  172,  or  the  dew-point  may  be  found  and  the  value  of  0.378*  taken  from  Table  172. 


.  h 

h 

760 

1 

2 

3 

0.0013158 
.0026316 
.0039474 

4 

I 

0.0052632 
.0065789 
.0078947 

7 
8 
9 

0.0092105 
.0105263 
.0118421 

EXAMPLES  OF  USE  OF  THE  TABLE. 


To  find  the  value  of  —  when  h  —  754.3 

h  —  700  gives  .92105 
50       '     .065789 
4  .005263 

.3    "      .000395 


754-3 


.992497 


To  find  the  value  of  —  when  h  —  5.73 

h  —  5  gives  .0065789 
.7  '  .0007895 
.03  .0000395 


5-73 


.0074079 


TABLE  175.  —Values  of  the  logarithms  of  „"„  for  values  of  h  between  80  and  340. 

:  from  the 
racteristic,  and  so  on. 


Values  from  8  to  80  may  be  got  by  subtracting  i  from  the  characteristic,  and  from  0.8  to  8  by  subtracting  2  from  the 

chara 


h 

Values  of  log  A. 
760 

0 

i 

2 

3 

4 

6 

6 

7 

8 

9 

80 

90 

T.O2228 
•07343 

1.02767 
.07823 

1.03300 
.08297 

7.03826 
.08767 

7.04347 
.09231 

7.04861 
.09691 

7.05368 
.10146 

7.05871 
.10596 

7.06367 
.11041 

7.o68;8 
.11482 

100 

1.11919 

7.12351 

1.12779 

1.13202 

7.13622 

7.14038 

7.14449 

7.14857 

7.15261 

7.15661 

no 

.16058 

.16451 

.16840 

.17226 

.17609 

.17988 

.18364 

.18737 

.19107 

•19473 

120 

•19837 

.20197 

•20555 

.20909 

.21261 

.21611 

.21956 

.22299 

.22640 

.22978 

130 

•233T3 

.23646 

•23976 

.24304 

.24629 

•24952 

•23273 

•25591 

.25907 

.26220 

140 

•26531 

.26841 

.27147 

.27452 

•27755 

.28055 

•28354 

.28650 

•28945 

.29237 

150 

7.29528 

1.29816 

1.30103 

7.30388 

7.30671 

7.30952 

7.31231 

7-3  !  509 

7.31784 

7.32058 

160 

•32331 

.32616 

.32870 

.33137 

•33403 

.33667 

•33929 

.34190 

•34450 

•34707 

170 
1  80 

.34964 
•37446 

.35218 
.37686 

•35471 
•37926 

•35723 
.38164 

•35974 
.38400 

.36222 
•38636 

.36470 
.38870 

.36716 
.39128 

.36961 
•39334 

•37204 
•39565 

190 

•39794 

.40022 

.40249 

.40474 

.40699 

.40922 

.41144 

•41365 

•41585 

.41804 

200 

1.42022 

1.42238 

1.42454 

7.42668 

7.42882 

7.43094 

7.43305 

7.435J6 

M3725 

7-43933 

2IO 

.44141 

•44347 

•44552 

•44757 

.44960 

.45162 

•45364 

•45565 

.45764 

•45963 

220 

.46161 

.46358 

.4^  e  C4 

.46749 

•46943 

•47137 

•47329 

•47521 

.47712 

.47902 

230 

.48091 

.48280 

.48467 

.48654 

.48840 

.49025 

.49210 

•49393 

•49576 

•4975s 

240 

.49940 

.50120 

.50300 

.50479 

.50658 

•50835 

.51012 

.51188 

.51364 

•5T539 

250 

J-sl7i3 

1.51886 

T.52059 

7.52231 

7.52402 

7-52573 

7.52743 

7.52912 

f.  5  308  1 

7.53249 

260 

•53416 

•53583 

•53749 

•539H 

•54079 

•54243 

•54407 

•54570 

•54732 

.54894 

270 

•55055 

•55216 

•55376 

•55535 

•55694 

•55852 

.56010 

.56167 

•56323 

.56479 

280 
290 

•56634 
.58158 

.56789 
.58308 

•56944 
•58457 

•57097 
•58605 

•57250 
•58753 

•57403 
.58901 

•57555 
.59048 

•57707 
.59194 

•57858 
•59340 

.58008 
.59486 

300 

7.59631 

7-59775 

1.59919 

7.60063 

7.60206 

7.60349 

7.60491 

7.60632 

7.60774 

7.60914 

310* 

•61055 

.61195 

•6i334 

•6i473 

.61611 

•61750 

.61887 

.62025 

.62161 

.62298 

320 

.62434 

.62569 

.62704 

.62839 

•62973 

.63107 

.63240 

•63373 

.63506 

.63638 

330 

•63770 

.63901 

.64032 

.64163 

.64293 

•64423 

•64553 

.64682 

.64810 

.64939 

340 

.65067 

.65194 

•65321 

•65448 

•65574 

.65701 

.65826 

•65952 

.66077 

.66201 

SMITHSONIAN  TABLES. 


162 


TABLE  175, 


DENSITY   OF   AIR. 


Values  of  logarithms  of  —  for  values  of  h  between  350  and  800. 


h 

Values  of  log  A. 
760 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

350 

7.66325 

1.66449 

7.66573 

7.66696 

1.66819 

1.66941 

1.67064 

7.67185 

7.67307 

7.67428 

360 

•67549 

.67669 

.67790 

.67909 

.68029 

.68148 

.68267 

.68385 

.68503 

.68621 

370 

.68739 

.68856 

.68973 

.69090 

.69206 

.69322 

•69437 

•69553 

.69668 

.69783 

380 

.69897 

.70011 

.70125 

.70239 

•70352 

.70465 

.70690 

.70802 

•709*4 

390 

.71025 

.71136 

.71247 

•71358 

.71468 

•7*578 

•7*688 

.71798 

.71907 

.72016 

400 

7.72125 

7.72233 

7.72341 

7.72449 

7.72557 

7.72664 

7.72771 

1.72878 

7.72985 

7.73091 

410 

•73*97 

•73303 

.73408 

•735*4 

•736*9 

•73723 

.73828 

•73932 

.74036 

•74*40 

420 

.74244 

•74347 

•7445° 

•74553 

.74655 

•7475s 

.74860 

.74961 

•7  5063 

.75*64 

43° 

•75265 

•75366 

•75467 

•75567 

.75668 

.75768 

.75867 

•75967 

.76066 

.76165 

440 

.76264 

.76362 

.76461 

•76559 

•76657 

•76755 

.76852 

.76949 

.77046 

•77*43 

450 

1.77240 

7.77336 

7.77432 

7.77528 

7.77624 

1.77720 

7.77815 

1.77910 

1.78005 

1.78100 

460 

.78194 

.78289 

.78383 

•78477 

•78570 

.78664 

.78757 

.78850 

.78943 

.79036 

470 

.79128 

.79221 

•79405 

•79496 

.79588 

.79679 

.79770 

.78961 

.79952 

480 

.80043 

.80133 

.80223 

•80313 

.80403 

.80493 

.80582 

.80672 

.80761 

.80850 

49° 

.80938 

.81027 

.81115 

.81203 

.81291 

.81379 

.81467 

•81554 

.81642 

.81729 

500 

T.8i8i6 

1.81902 

1.81989 

7.82075 

1.82162 

1.82248 

7.82334 

1.82419 

7.82505 

1.82590 

520 
530 
540 

.82676 

•835*9 
.84346 
.85*58 

.82761 
.83602 
.84428 
•85238 

.82846 
.83686 
•845*0 
•853*9 

.82930 
.83769 
.84591 
•85399 

•83015 
.83852 
•84673 
.85479 

.83099 
.83935 
•84754 
.85558 

.83*84 
.84017 

•84835 
•85638 

.83268 
.84100 
.84916 
•857*7 

.83352 
.84182 
.84997 
.85797 

•83435 
.84264 
•85076 
•85876 

550 

7.85955 

1.86034 

i.  86113 

1.86191 

1.86270 

1.86348 

1.86426 

1.86504 

1.86582 

7.8666o 

560 

•86737 

.86815 

.86892 

.86969 

•87047 

.87123 

.87200 

•87277 

•87353 

.87430 

57° 

.87282 

.87658 

•87734 

.87810 

.87885 

.87961 

.88036 

.88111 

.88186 

580 

.88261 

.88336 

.88411 

.88486 

.88560 

.88634 

.88708 

.88782 

.88856 

.88930 

590 

.89004 

.89077 

•8915* 

.89224 

.89297 

•89370 

.89443 

.89516 

.89589 

.89661 

600 

610 
620 

7.89734 
.90452 
.91158 

1.89806 

•90523 
.91228 

1.89878 
•90594 
.91298 

7.89950 
.90665 
.91367 

1.90022 
•90735 
•9*437 

1.90094 
.90806 
•91507 

1.90166 

•90877 
•9*576 

7.90238 
•90947 
•9*645 

7.90309 
.91017 

•9*7*5 

1.90380 
.91088 
•9*784 

630 
640 

•9*853 
•92537 

.91922 

.92604 

•9*990 
.92672 

•92059 
.92740 

.92128 
.92807 

.92196 
.92875 

.92264 
.92942 

•92333 
•93009 

.92401 
•93076 

.92469 
•93*43 

650 

660 
670 

1.93210 

•93873 
•94526 

7.93277 
•93930 
•9459* 

7-93343 
.94004 
•94656 

7.934io 

.94070 
•94720 

7.93476 
•94*35 
•94785 

7-93543 
.94201 
.94849 

1.93601 
.94266 
•949*3 

7.93675 
•9433* 
.94978 

7-9374* 
•94396 
•95042 

7.93807 
.94461 
.95*o6 

680 
690 

•95*70 
.95804 

•95233 
.95866 

•95297 
•95929 

.95992 

.95424 
•96055 

.95488 
.96117 

•9555* 

.95614 
.96242 

•95677 
.96304 

•9574* 
.96366 

700 

1.96428 

1.96490 

7-96552 

1.96614 

1.96676 

7.96738 

7.96799 

1.96861 

1.96922 

7.96983 

710 
720 

73° 
740 

•97044 
.97652 
.98251 
.98842 

.97106 
•977*2 
.98310 
.98900 

.97167 
•97772 
.98370 
.98959 

.97228 
•97832 
.98429 
.99018 

.97288 
•97892 
.98488 
.99076 

•97349 
•9795* 
•98547 
•99*34 

•974*0 
.98012 
•  .98606 
•99*93 

.9747* 
.98072 
.98665 
•9925* 

•9753* 
.98132 

.98724 
.99309 

•97592 
.98191 
.98783 
.99367 

750 

760 

7.99425 

o.ooooo 

7.99483 
0.00057 

7-99540 
0.00114 

7.99598 
0.00171 

7.99656 
0.00228 

7-997*3 
0.00285 

7-9977* 
0.00342 

1.99828 
0.00398 

1.99886 
0.00455 

7.99942 
0.00511 

770 
780 

.00568 

.01128 

.0062^ 
.0118, 

.00680 
.01239 

.00737 
.01295 

.00793 
•0135° 

.00849 
.01406 

.00905 
.01461 

.00961 
.01516 

.01017 
.01571 

.01072 
.01626 

790 

.01681 

•01736 

.01791 

.01846 

.01901 

•0*955 

.02010 

.02064 

.02119 

.02173 

SMITHSONIAN  TABLES. 


163 


TABLE  176. 


VOLUME   OF    PERFECT   CASES. 


Values  of  1  +  . 00367*. 

The  quantity  i  +  -00367 1  gives  for  a  perfect  gas  the  volume  at  t°  when  the  pressure 
is  kept  constant,  or  the  pressure  at  t°  when  the  volume  is  kept  constant,  in  terms, 
of  the  volume  or  the  pressure  at  o°. 

(a)  This  part  of  the  table  gives  the  values  of  i  +  .00367 1  for  values  of  t  between  o° 
and  10°  C.  by  tenths  of  a  degree. 

(b)  This  part  gives  the  values  of  i  +  .00367 1  for  values  of  /  between  — 90°  and  +  1990° 
C.  by  10°  steps. 

These  two  parts  serve  to  give  any  intermediate  value  to  one  tenth  of  a  degree  by  a  sim- 
ple computation  as  follows: — In  the  (£)  table  find  the  number  corresponding  to 
the  nearest  lower  temperature,  and  to  this  number  add  the  decimal  part  of  the 
number  in  the  (a)  table  which  corresponds  to  the  difference  between  the  nearest 
temperature  in  the  (b)  table  and  the  actual  temperature.  For  example,  let  the 
temperature  be  682°. 2  : 

We  have  for  680  in  table  (A)  the  number  ....     3.49560 

And  for  2.2  in  table  (a)  the  decimal .00807 

Hence  the  number  for  682. 2  is 3-5°367 

(C)  This  part  gives  the  logarithms  of  i  +  . 00367^  for  values  of  t  between — 49°  and 

+  399°  C.  by  degrees. 

(d)  This  part  gives  the  logarithms  of  i  +  -00367 1  for  values  of  t  between  400°  and  1990° 
C.  by  10°  steps. 

(a)  Values  of  1  +  . 00367 1  for  Values  of  /  between  0°  and  10°  G.  by  Tenths 
of  a  Degree. 


* 

0.0 

0.1 

0.2 

0.3 

0.4 

0 

1.  00000 

1.00037 

1.00073 

I.OOIIO 

1.00147 

I 

.00367 

.00404 

.00440 

.00477 

•00514 

2 

.00734 

.00771 

.00807 

.00844 

.00881 

3 

.01101 

.01138 

.01174 

.OI2II 

.01248 

4 

.01468 

•01505 

.01541 

.01578 

.01615 

5 

1.01835 

1.01872 

1.01908 

I.OI945 

1.01982 

6 

.02202 

.02239 

.02275 

.O23I2 

.02349 

7 

.02569 

.02606 

.02642 

.02679 

.02716 

8 

.02936 

.02973 

.03009 

.03046 

.03083 

9 

•03303 

•03340 

•03376 

•03413 

.03450 

t 

0.5  * 

0.6 

0.7 

0.8 

0.9 

0 

1.00184 

i.  002  20 

1.00257 

1.00294 

1.00330 

i 

.00550 

.00587 

.00624 

.00661 

.00697 

2 

.00918 

.00954 

.00991 

.01028 

.01064 

3 

.01284 

.01321 

•01358 

•or395 

.01431 

4 

.01652 

.01688 

.01725 

.01762 

.01798 

5 

1.02018 

1.02055 

1.02092 

1.02129 

1.02165 

6 

.02386 

.02422 

.02459 

.02496 

.02532 

7 

.02752 

.02789 

.02826 

.02863 

.02899 

8 

.03120 

•03156 

•03*93 

.03290 

.03266 

9 

.03486 

•03523 

.03560 

•03597 

•03633 

SMITHSONIAN  TABLES. 


164 


TABLE  176. 


VOLUME    OF   PERFECT   CASES. 


(b)  Values  of  1  +  .00367  f  for  Values  of  /  between  —90°  and  +  1990°  0.  by 
10°  Steps. 


t 

00 

10 

20 

30 

40 

—000 

I.OOOOO 

0.96330 

0.92660 

0.88990 

0.85320 

+000 

1.  00000 

1.93670 

1.07340 

I.IIOIO 

1.14680 

IOO 

1.36700 

1.40370 

1.44040 

1.44710 

1.51380 

200 

1.73400 

1.77070 

1.80740 

1.84410 

1.88080 

300 

2.IOIOO 

2.13770 

2.17440 

2.21  1  10 

2.24780 

400 

2.46800 

2.50470 

2.54140 

2.57810 

2.61480 

500 

2.83500 

2.87170 

2.90840 

2.94510 

2.98180 

600 
700 
800 

3.20200 

3.56900 
3.93600 

3.23870 
3.60570 
3.97270 

3-2754° 
3.64240 
4.00940 

3.3I2IO 
3.67910 
4.04610 

3.34880 

3-7I580 
4.08280 

900 

4.30300 

4-3397° 

4.37640 

4.41310 

4.44980 

1000 

4.67000 

4.70670 

4-74340 

4.78010 

4.81680 

IIOO 

5.03700 

5-07370 

5.11040 

5.I47IO 

5.18380 

1  200 

5.40400 

5.44070 

5-47740 

5.51410 

5.55080 

1300 
1400 

5.77100 

6.13800 

5.80770 
6.17470 

5.84440 
6.21140 

5.88IIO 
6.24810 

5.91780 
6.28480 

1500 

1600 

6.50500 

6.87200 

6.54170 
6.90870 

6.57840 
6.94540 

6.61510 
6.98210 

6.65180 
7.01880 

1700 

7.23900 

7.27570 

7.31240 

7.34910 

7.38580 

1800 

7.60600 

7.64270 

7.67940 

7.7l6lO 

7.75280 

1900 

7.97300 

8.00970 

8.04640 

8.08310 

8.11980 

2000 

8.34000 

8.37670 

8.41340 

8.45OIO 

8.48680 

t 

50 

60 

70 

80 

90 

-000 

0.81650 

0.77980 

0.74310 

0.70640 

0.66970 

+000 

1.18350 

I.22O2O 

1.25690 

1.29360 

I-33030 

IOO 

1.58720 

1.62390 

1.66060 

1.69730 

200 

1.91750 

1.95420 

1.99090 

2.02760 

2.06430 

300 

2.28450 

2.32120 

2.55790 

2.39460 

2.43130 

400 

2.65150 

2.68820 

2.72490 

2.76160 

2.79830 

500 

3.01850 

3-05520 

3.09190 

3.12860 

3-  i  6530 

600 

3-3855° 

3.4222© 

3-45890 

3.49560 

3-53230 

700 

3-75250 

3.7*8920 

3.82590 

3.86260 

3-89930 

800 

4.11950 

4.15620 

4.19290 

4.22960 

4.26630 

900 

4.48650 

4.52320 

4-55990 

4.59660 

4-63330 

10OO 

4-85350 

4.89020 

4.92690 

4.96360 

5.00030 

IIOO 

5.22050 

5.25720 

5-29390 

5-33°6° 

5-3673° 

1200 

1300 
1400 

5-58750 

5-9545° 
6.32150 

5.62420 
5.99120 
6.35820 

5.66090 
6.02790 
6.39490 

5.69760 
6.06460 
6.43160 

5-7343° 
6.10130 
6.46830 

1500 

6.68850 

6.72520 

6.76190 

6.79860 

6.83530 

1600 

7-°555° 

7.09220 

7.12890 

7.16560 

7.20230 

1700 

7.42250 

745920 

7.49590 

7.53260 

7.56930 

1800 

7.78950 

7.82620 

7.86290 

7.89960 

7-9363° 

1900 

8.15650 

8.19320 

8.22990 

8.26660 

8.3°33° 

2000 

8.5235° 

8.56020 

8.59690 

8.63360 

8.67030 

SMITHSONIAN  TABLES. 


165 


TABLE  176 


VOLUME   OF 

(c)  Logarithms  of  1  +  .00367 1  for  Values 


* 

0 

1 

2 

3 

4 

Mean  diff. 
per  degree. 

—  40 

1.931051 

1.929179 

1.927299 

1.925410 

^•923513 

1884 

—  3° 

•949341 

•947546 

•945744 

•943934 

.942117 

1805 

—  20 
—  10 

.966892 
.983762 

.965169 
.982104 

.963438 
.980440 

.961701 
.978769 

•959957 
.977092 

1733 
1667 

—  o 

o.oooooo 

.998403 

.996801 

.995192 

•993577 

1605 

+  0 

0.000000 

0.001591 

0.003176 

0.004755 

0.006329 

1582 

10 

•OI5653 

.017188 

.018717 

.020241 

.021760 

1526 

20 
3° 

.030762 
.045362 

.032244 
.046796 

.033721 
.048224 

.035193 
.049648 

.036661 
.051068 

1474 
1426 

40 

.059488 

.060875 

.062259 

.063637 

.065012 

1381 

50 

0.073168 

0.074513 

0-075853 

0.077190 

0.078522 

1335 

60 

.086431 

•087735 

.089036 

.090332 

.091624 

I299 

1° 

.099301 

.100567 

.101829 

.103088 

.104344 

1259 

80 

.111800 

.113030 

.114257 

.115481 

.116701 

1226 

90 

.123950 

.125146 

.126339 

.127529 

.128716 

II9I 

100 

0.135768 

0-136933 

0.138094 

0.139252 

0.140408 

1158 

no 

.147274 

.248408 

•149539 

.150667 

•i5!793 

1129 

120 

.158483 

.159588 

.160691 

.161790 

.162887 

IIOI 

130 

.169410 

.170488 

•171563 

.172635 

.173705 

1074 

140 

.180068 

.181120 

.182169 

.183216 

.184260 

1048 

150 

0.190472 

0.191498 

0.192523 

0.193545 

0.194564 

IO23 

160 

.200632 

.201635 

.202635 

.203634 

.204630 

1000 

170 

.210559 

.211540 

.212518 

.213494 

.214468 

976 

1  80 

.220265 

.221224 

.222180 

•223135 

.224087 

956 

190 

.229959 

.230697 

•231633 

•232567 

•233499 

935 

200 

0.239049 

0.239967 

0.240884 

0.241798 

0.242710 

916 

2IO 

.248145 

.249044 

.249942 

.250837 

•25I731 

897 

220 

.257054 

.257935 

.258814 

.259692 

.260567 

878 

230 

.265784 

.266648 

.267510 

.268370 

.269228 

861 

24O 

•274343 

.275189 

•276034 

.276877 

.277719 

844 

250 

0.282735 

0.283566 

0-284395 

0.285222 

0.286048 

828 

260 

.290969 

.291784 

.292597 

.293409 

.294219 

813 

270 

.299049 

.299849 

.300648 

.301445 

.302240 

798 

280 

.306982 

.307768 

.308552 

•309334 

•3IO«S 

784 

290 

•3J4773 

•315544 

•3I63H 

•3  !  7083 

•3*7850 

769 

300 

0.322426 

0.323184 

0.323941 

0.324696 

0.32545° 

756 

310 

•329947 

.330692 

•33H35 

•332178 

•3329!9 

743 

320 

•337339 

.338072 

•338803 

•339533 

.340262 

73° 

330 

.344608 

•345329 

•345048 

.346766 

.347482 

719 

340 

•351758 

.352466 

•353174 

•353880 

•354585 

707 

350 

o-35879i 

0.359488 

0.360184 

0.360879 

0-361573 

696 

360 

•3657i3 

.366399 

.367084 

.367768 

.368451 

684 

370 

•372525 

.373201 

•373875 

•374549 

•375221 

674 

380 

•379233 

.379898 

•380562 

.381225 

.381887 

664 

390 

•385439  > 

.386494 

.387148 

.387801 

.388453 

654 

SMITHSONIAN  TABLES. 


1 66 


TABLE  176, 


PERFECT   CASES. 

ol  t  between  —49°  and  +399°  0.  by  Degrees. 


I 

5 

6 

7 

8 

9 

Mean  diff. 
per  degree. 

—  40 

1.921608 

1.919695 

1.917773 

7.915843 

1.913904 

1926 

—  3° 

—  20 

.940292 
.958205 

.938460 
.956447 

.936619 
•954681 

•93477  * 
•952909 

.932915 
.951129 

1845 
1771 

—  10 

•975409 

•973719 

.972022 

.970319 

.968609 

1699 

—  O 

•99  r  957 

.990330 

.988697 

•987058 

•985413 

1636 

+  0 

10 

0.007897 
.023273 

0.009459 
.024781 

0.011016 
.026284 

0.012567 
.027782 

0.014113 

.029274 

1554 

1500 

20 

.038123 

.039581 

.041034   . 

.042481 

.043924 

*45o 

3° 
40 

.052482 
.066382 

.053893 
.067748 

.055298 
.069109 

.056699 
.070466 

.058096 
.071819 

1402 
*359 

50 

0.079847 

0.081174 

0.082495 

0.083811 

0.085123 

I3I5 

60 

.092914 

.094198 

.095516 

.096715 

.098031 

1281 

70 

•I05595 

.106843 

.108088 

.109329 

.110566 

1243 

80 

.117917 

.119130 

.120340 

.121547 

.122750 

1210 

90 

.129899 

.131079 

.132256 

•133430 

.134601 

"75 

100 

0.141559 

0.142708 

0.143854 

0.144997 

0.146137 

1144 

110 

1  20 

.152915 
.163981 

•'54034 
.164072 

.155151 
.166161 

.156264 
.167246 

•'57375 
.168330 

IIJ5 

1087 

130 

.174772 

•175836 

.176898 

•177958 

.179014 

1060 

140 

.185301 

.186340 

•J87377 

.188411 

.189443 

'035 

150 

0.195581 

0.196596 

0.197608 

0.198619 

0.199626 

IOII 

1  60 

.205624 

.206615 

.207605 

.208592 

.209577 

988 

170 
1  80 

•215439 

.225038 

.216409 
.225986 

•217376 
.226932 

.218341 
.227876 

.219904 
.228819 

966 
946 

190 

.234429 

•235357 

.236283 

•237207 

.238129 

925 

200 

0.243621 

0.244529 

0.245436 

0.246341 

0.247244 

906 

2IO 

.252623 

•253512 

.254400 

•255287 

.256172 

887 

2  2O 

.261441 

.262313 

.263184 

.264052 

.264919 

870 

230 
240 

.270085 
•278559 

.270940 
•279398 

.271793 
.280234 

.272644 
.281070 

•273494 
.281903 

853 
836 

250 

0.286872 

0.287694 

0.288515 

0.289326 

0.290153 

820 

260 

.295028 

•295835 

.296860 

•297445 

.298248 

805 

270 

•303034 

.303827 

.304618 

•305407 

.306196 

790 

280 

.310895 

.311673 

•3I245° 

.313226 

.314000 

776 

290 

.318616 

•3T93Si 

.320144 

.320906 

.321667 

763 

300 

0.326203 

0.326954 

0.327704 

0.328453 

0.329201 

750 

310 

•333659 

•334397 

•335T35 

•33587i 

•336606 

737 

320 

.340989 

•34I7IS 

.342441 

•343  1  64 

.343887 

724 

33° 

.348198 

.348912 

.349624 

•350337 

.351048 

713 

340 

•355289 

•355991 

•356693 

•357394 

•358093 

701 

350 

0.362266 

0.362957 

0.363648 

0.364337 

0.365025 

690 

360 

.369132 

.369813 

•370493 

.371171 

.371849 

678 

370 

.375892 

•376562 

•377232 

•377900 

•378567 

668 

380 

.382548 

.383208 

.383868 

•384525 

.385183 

658 

390 

.389104 

•389754 

.390403 

.391052 

.39  [699 

648 

SMITHSONIAN  TABLES. 


167 


TABLE  176. 

VOLUME    OF    PERFECT   CASES. 

( d)  Logarithms  of  1  +  .00367 1  for  Values  of  t  between  400°  and  1990°  C.  by  10°  Steps. 


t 

00 

10 

20 

30 

40 

400 

0.392345 

0.398756 

0.405073 

0.411300 

0.417439 

500 

0-452553 

0.458139 

0.463654 

0.469100 

0-474479 

600 

.505421 

•5I037i 

.515264 

.520103 

.524889 

700 

•552547 

•55699o 

.561388 

.565742 

.570052 

800 
900 

•595055 
•633771 

.599086 
.637460 

.603079 
.641117 

.607037 
•644744 

.610958 
.648341 

1000 

0.669317 

0.672717 

0.676090 

0-679437 

0.682759 

IIOO 

.702172 

•705325 

•708455 

•7II563 

.714648 

1200 

•732715 

•735655 

•738575 

•741745 

.744356 

1300 

.761251 

.764004 

.766740 

•769459 

.772160 

I4OO 

.788027 

.790616 

.793190 

.795748 

.798292 

1500 

1600 

0.813247 
.837083 

0.815691 
•839396 

0.818120 
.841697 

0.820536 
.843986 

0.822939 
.84626} 

1700 

.839679 

.861875 

.864060 

.866234 

.868398 

1800 

.881156 

.883247 

•885327 

.887398 

.889459 

1900 

.901622             .903616 

.905602 

.907578 

•909545 

t 

50 

60 

70 

80 

90 

400 

0.423492 

0.429462 

0.435351 

0.441161 

0.446894 

500 

0.479791 

0.485040 

0.49022? 

0-495350 

0.500415 

600 

.529623 

•53430.5 

•538938 

•543522 

•548058 

700 

•574321 

•578548 

.582734 

.586880 

.590987 

800 
900 

.614845 
.651908 

.618696 
•655446 

•622515 
•658955 

.626299 
.662437 

.630051 
.665890 

1000 

0.686055 

0.689327 

0.692574 

0-695797 

0.698996 

IIOO 

.717712 

•720755 

.723776 

.726776 

.729756 

1  200 
1300 

.747218 
.774845 

.750061 
•7775*4 

.752886 
.780166 

•755692 
.782802 

.758480 
.785422 

1400 

.800820 

•803334 

.805834 

.808319 

.810790 

1500 

0.825329 

0.827705 

0.830069 

0.832420 

0.834758 

1600 

.848828 

.850781 

•853023 

•855253 

•857471 

1700 

.870550 

.872692 

.874824 

.876945 

.879056 

1800 

.891510 

•893551 

•895583 

-897605 

.899618 

1900 

.911504 

•913454 

•915395 

.917327 

.919251 

SMITHSONIAN  TABLES. 


168 


TABLE  177. 


DETERMINATION  OF  HEIGHTS  BY  THE   BAROMETER. 


Formula  of  Babinet :  Z  =  C 
C  (in  feet)  =  52494  [z  -f- 


900 


BO  +  B 

English  measures. 


C  (in  metres)  =:  16000      i  -f-  2     °        '  1  metric  measures. 
L-  1000     -I 

In  which  Z  =:  difference  of  height  of  two  stations  in  feet  or  metres. 
J50,  B  —  barometric  readings  at  the  lower  and  upper  stations  respectively,  corrected  for  all 

sources  of  instrumental  error. 
t0,  t  —  air  temperatures  at  the  lower  and  upper  stations  respectively. 

Values  of  C. 


ENGLISH  MEASURES. 

METRIC  MEASURES. 

l%+6 

C 

LogC 

M'o  +  0. 

C 

LogC 

Fahr. 

Feet. 

Cent. 

Metres. 

10° 

49928 

4.69834 

—10° 

15360 

4.18639 

15 

5051  1 

•70339 

—8 

15488 

.19060 

—6 

15616 

•!9357 

20 

5I094 

4.70837 

—4 

15744 

.19712 

25 

5l677 

.71330 

—  2 

15872 

.20063 

30 

52261 

4.71818 

0 

16000 

4.20412 

35 

52844 

.72300 

+  2 

16128 

.20758 

4 

16256 

.2IIOI 

40 

53428 

4.72777 

6 

16384 

.21442 

45 

54011 

.73248 

8 

16512 

.21780 

50 

54595 

4-737I5 

10 

16640 

4.22115 

55 

55178 

•74177 

12 

16768 

.22448 

14 

16896 

.22778 

60 

5576i 

4-74633 

16 

17024 

.23106 

65 

56344 

.75085 

18 

17152 

•23431 

70 

56927 

4-75532 

20 

17280 

4.23754 

75 

575" 

•75975 

22 

17408 

.24075 

24 

17536 

.24393 

80 

58094 

4.76413 

26 

17664 

.24709 

85 

58677 

.76847 

28 

17792 

.25022 

90 

59260 

477276 

30 

I7920 

4-25334 

95 

59844 

•77702 

32 

18048 

.25643 

34 

18176 

•2595° 

100 

60427 

4.78123 

36 

18304 

•26255 

SMITHSONIAN  TABLES. 


169 


TABLE  178. 


BAROMETRI 

Barometric  pressures  corresponding  to  differs 
This  table  is  useful  when  a  boiling-point  apparatus  is  us 


(a)  British  Measure. 


Temp.  F. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

185° 

.      186 

17-05 
17.42 

17.08 
17.46 

17.12 
I7-50 

17.16 

17-54 

17.20 
I7-58 

17-23 
17.61 

17.27 
17-65 

'7-3i 
17.69 

17-35 
17-73 

17-39 

17.77 

187 

188 

17.81 
18.20 

17.84 
18.24 

17.88 
18.27 

17.92 
18.31 

17.96 
18.35 

18.00 
18.39 

18.04 
18.43 

18.08 
18.47 

18.12 
18.51 

18.16 
18-55 

189 

190 

18.59 

19.00 

18.63 
19.04 

18.67 
19.08 

18.71 
19.12 

18.75 
19.16 

18.79 
19.20 

18.83 
19.24 

18.87 
19.28 

18.91 
19.32 

18.95 
19.36 

191 

192 

19.41 
19.82 

19-45 
19.87 

19.49 
19.91 

19-53 
'9-95 

19-57 
19.99 

19.61 

20.04 

19.66 

20.08 

19.70 

2O.  I  2 

19.74 
20.17 

19.78 

2O.2I 

193 

194 

20.25 
20.68 

20.29 
20.73 

20.34 
20.77 

20.38 
20.82 

20.42 
20.86 

20.47 
20.90 

20.51 
20.95 

20-55 
20.99 

20.60 
21.04 

20.64 
2  1.  08 

195 

196 

21.13 

21.58 

21.17 
21.62 

21.22 
21.67 

21.26 
21.71 

21.30 
21.76 

21-35 
21.80 

21.39 

21.85 

21.44 
21.89 

21.48 
21.94 

21-53 
21.99 

197 

198 

22.03 

22.50 

22.08 
22.54 

22.12 
22-59 

22.17 
22.64 

22.22 
22.69 

22.26 
22.73 

22.31 

22.78 

22.36 
22.83 

22.40 

22.88 

22.45 
22.92 

199 

200 

22.97 
23-45 

23.02 
23-50 

23.07 
23-55 

23.11 
23.60 

23.16 
23-65 

23.21 
23.70 

23.26 
2375 

23.31 
23.80 

23.36 
23.85 

23.40 
23.89 

201 

202 

23-94 
24.44 

23-99 
24.49 

24.04 
24-54 

24.09 
24-59 

24.14 
24.64 

24.19 
24.69 

24.24 
24.74 

24.29 
24.80 

24-34 
24.85 

24-39 
24.90 

203 

204 

24-95 
25.46 

25.00 
25-52 

25-05 
25-57 

25.10 
25.62 

25.15 
25.67 

25.21 
25-73 

25.26 
25.78 

25-31 
25-83 

*$ 

25.41 
25-94 

205 

206 

25-99 
26.52 

26.04 
26.58 

26.IO 
26.63 

26.15 
26.68 

26.2O 
26.74 

26.25 
26.79 

26.31 
26.85 

26.36 
26.90 

26.42 
26.96 

26.47 

27.01 

207 

208 

27.07 
27.62 

27.12 
27.67 

27.18 
27-73 

27.23 
27.79 

27.29 
27.84 

27-34 
27.90 

27.40 
27-95 

27-45 
28.01 

27/51 
28.07 

27.56 
28.12 

209 

2IO 

28.18 

28.75 

28.24 
28.81 

28.29 
28.87 

28.35 
28.92 

28.41 
28.98 

28.46 
29.04 

28.52 
29.10 

28.58 
29.16 

28.64 
29.21 

28.69 
29.27 

211 

212 

29-33 
29.92 

29-39 
29.98 

29-45 
30.04 

29.51 
30.10 

29-57 
30.16 

29.62 
30.22 

29.68 
30.28 

29.74 
30-34 

29.80 
30.40 

29.86 
30.46 

SMITHSONIAN   TABLES. 


170 


TABLE  178, 


PRESSURES. 

temperatures  of  the  boiling-point  of  water. 

in  place  of  the  barometer  for  the  determination  of  heights. 


Metric  Measure.* 


Temp.  C. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

80° 

354-6 

356-I 

357-5 

359-o 

360.4 

361.9 

363-3 

364.8 

366.3 

367.8 

81 

369-3 

370.8 

372-3 

373-8 

375-3 

376.8 

378.3 

379-8 

38L3 

382.9 

82 

384-4 

385-9 

387.5 

389.0 

390.6 

392-2 

393-7 

395-3 

396.9 

398.5 

83 

400.1 

401.7 

403.3 

404.9 

406.5 

408.1 

409.7 

4i  i-3 

413.0 

414.6 

84 

416.3 

417.9 

419.6 

421.2 

422.9 

424.6 

426.2 

427.9 

4296 

43!-3 

85 

433-0 

434-7 

436-4 

438.1 

439-9 

441.6 

443-3 

445.1 

446.8 

448.6 

86 

450-3 

452.1 

453-8 

455-6 

457-4 

459-2 

461.0 

462.8 

464.6 

466.4 

87 

468.2 

470.0 

471.8 

473-7 

475-5 

477-3 

479-2 

481.0 

482.9 

484.8 

88 

486.6 

488.5 

490.4 

492.3 

494-2 

496.1 

498.0 

499-9 

501.8 

503.8 

89 

505-7 

507-6 

509.6 

5".5 

5!3-5 

515.5 

Sl7-4 

519.4 

521.4 

523-4 

90 

5254 

5274 

529-4 

531-4 

533-4 

535-5 

537-5 

539-6 

541.6 

543-7 

9i 

545-7 

547-8 

549-9 

55J-9 

554-0 

556.1 

558.2 

560.3 

562.4 

564.6 

92 

566-7 

568.8 

57i-o 

573-1 

575-3 

577-4 

579-6 

581.8 

584-0 

586.1 

93 

588.3 

590-5 

592.7 

595-0 

597-2 

599-4 

601.6 

603.9 

606.1 

608.4 

94 

610.7 

612.9 

615.2 

6i7-5 

619.8 

622.1 

624.4 

626.7 

629.0 

631.4 

95 

633-7 

636.0 

638-4 

640.7 

643.1 

645-5 

647-9 

650.2 

652.6 

655.0 

96 

6574 

659-9 

662.3 

664-7 

667.1 

669.6 

672.0 

674.5 

677.0 

679.4 

97 

681.9 

6844 

686.9 

689.4 

691.9 

694.5 

697.0 

699.5 

702.1 

704.6 

98 

707.2 

709.7 

712.3 

714.9 

7I7-5 

720.1 

722.7 

725-3 

727-9 

730-5 

99 

733-2 

735-8 

738.5 

741.2 

743-8 

746.5 

749-2 

75I>9 

754-6 

757.3 

100 

760.0 

762.7 

765-5 

768.2 

770.9 

773-7 

776.5 

779.2 

782.0 

784-8 

SMITHSONIAN  TABLES. 


*  Pressures  in  millimetres  of  mercury. 
171 


TABLE  179. 


STANDARD  WAVE-LENGTHS. 

This  table  is  an  abridgment  of  the  table  published  by  Rowland  (Phil.  Mag.  [5]  vol.  36,  pp.  49-75).  The  first  column 
gives  the  number  of  the  line  reckoned  from  the  beginning  of  Rowland's  table,  and  thus  indicates  the  number  of 
lines  of  the  table  that  have  been  omitted.  The  second  column  gives  the  chemical  symbol  of  the  element  repre- 
sented by  the  line  of  the  spectrum.  The  third  column  indicates  approximately  the  relative  intensity  of  the  lines 
recorded  and  also  their  appearance;  R  stands  for  reversed,  d  for  double,  ?  for  doubtful  or  difficult.  The  fourth 
column  gives  the  relative  "  weights  "  to  be  attached  to  the  values  of  the  wave-lengths  as  standards.  The  last 
column  gives  the  values  of  the  wave-lengths  in  Angstrom's  units,  i.  e.,  in  ten  million ths  of  a  millimetre  in  ordinary 
air  at  about  20°  C.  and  760  millimetres  pressure.  When  two  or  more  elements  are  on  the  same  line  of  the  table 
it  indicates  that  they  have  apparently  coincident  lines  in  the  spectrum  for  that  wave-length.  When  two  or  more 
lines  are  bracketed  it  means  that  the  first  one  has  a  line  coinciding  with  one  side  of  the  corresponding  line  in  the 
solar  spectrum  and  so  on  in  order.  Lines  marked  A(o)  and  A(wv)  denote  lines  due  to  absorption  by  the  oxygen 
or  water  vapor  in  the  earth's  atmosphere.  The  letters  placed  in  front  of  some  of  the  numbers  in  the  first  column 
are  the  symbols  of  well-known  lines  in  the  spectrum.  The  footnotes  are  from  Rowland's  paper. 


No.  of 
line. 

Element. 

Inten- 
sity and 
appear- 
ance. 

Weight. 

Wave- 
length (arc 
spectrum). 

No.  of 
line. 

Element. 

Inten- 
sity and 
appear- 
ance. 

Weight. 

Wave- 
length (arc 
spectrum). 

I 

Sr 

2 

I 

2152.912 

"5 

Fe 

10  A* 

4 

2937.020 

4 
7 

Si 
Si 

3 

2 

2 
2 

2210.939 
2218.146 

117 

121 

Fe 
Fe 

1R 
8R 

4 
12 

2954.058 
2967.016 

9 

Al 

4 

2 

2269.161 

124 

Fe 

12R 

15 

2973-358 

ii 

Ca 

.20  R 

3 

2275.602 

126 

Fe 

10  A3 

"5 

2983.689 

14 

Ba 

20  R 

I 

2335.267 

I29 

Fe 

SR 

18 

2994-547 

16 

Fe 

- 

2 

2348.385 

Ca 

loR 

3 

2997.430 

19 

Al 

7 

3 

2373-2I3 

135 

Fe 

SR 

15 

3001.070 

22 

Fe 

— 

2 

2388.710 

I36 

Ca 

i$R 

3 

3006.978 

24 

Ca 

25* 

5 

2398.667 

141 

Fe 

6R 

15 

3008.255 

151 

Fe 

2SR 

1  8 

3020.759 

29 

Si 

8 

15 

2435-247 

163 

Fe 

20  R 

13 

3047.720 

31 

Si 

3 

IO 

2443.460 

169 

Fe 

10  R 

15 

3059.200 

Si 

IO 

"*  i  "  "*    "M  n 

37* 
46 

C 
Bo 

10 

20 

15 

20 

2478.661 
2497.821 

(Sun 
spectrum.) 

136 

? 

3 

_ 

3005.160 

51 

Si 

15 

7 

2516.210 

144 

? 

4 

- 

3012.557 

ft 

Si 

Hg 

50  A' 

10 

2 

2524.206 

2  $36.648 

158 

\ 

5 

5 

7 
7 

3024.475 

3°35-85° 

63 

Al 

10 

5 

2568.085 

164 

? 

5 

3050.212 

68 

Mn 

— 

2 

2593.810 

171 

Co 

3 

5 

3061.930 

»73 

Si 

5 

7 

2631.392 

177 

Fe? 

4 

6 

3078.148 

77 

Fe 

— 

3 

2/120.989 

I87 

? 

2 

9 

3094.739 

78 

Ca 

5 

i 

2721.762 

197 

Vat 

5 

9 

3121.275 

82 

Fe 

3 

2742.485 

2O  I 

3 

5 

3140.869 

85 

Fe 

— 

3 

2756.427 

203 

Mn 

i 

5 

3167.290 

99 

Mg 

20  R 

12 

2795.632 

207 

Cr? 

4 

5 

3188.164 

IO2 

Mg 

20  R 

10 

2802.805 

209 

Ti 

4 

5 

3200.032 

1  06 

Fe 

4 

7 

2832.545 

211 

Ti 

3 

6 

3218.390 

III 
112 

Mg 
Si 

100  R 
'5 

15 

12 

2852.239 
2881.695  I 

215 
222 

Ti 
Cu 

4 
9 

3 

5 

3224.368 
3247.680 

*  Seems  to  be  the  only  single  carbon  line  not  belonging  to  a  band  in  the  arc  spectrum.    It  was  determined 

to  belong  to  carbon  by  the  spark  spectrum. 

t  This  line  appears  as  a  sharp  reversal,  with  no  shading,  in  the  spectra  of  all  substances  tried  that  contained 

any  trace  of  a  continuous  spectrum  in  the  region. 

t  There  is  a  faint  line  visible  on  the  violet  side. 

SMITHSONIAN  TABLES. 


1/2 


TABLE  179. 


STANDARD  WAVE-LENGTHS. 


No.  of 
Line. 

Element. 

Inten- 
sity anc 
apj>ear 
ance. 

Weight 

Wave- 
length (sun 
spectrum). 

No.  of 
Line. 

Element. 

Inten- 
sity anc 
appear- 
ance. 

(Weight 

Wave- 
length (sun 
spectrum). 

224 
229 
235 
239 
241 

Va 
Na 
Ti 
Zr 
Fe 

4 
6 

5 
i 

2 

10 
6 

10 

8 

12 

3267.839 
3302.501 

3356.222 
3389.887 

409! 
410 

417 

420 

422 

Fe? 
Fe 
Fe 
Mn 
Fe 

10 

3 
20 

5 
15 

3 
7 
7 
13 

7 

4005.305 
4016.578 

4045-975 
4055.701 
4063.756 

244 
250 

Fe 
Co 
Co,  Fe,  N 

4 
4 

4 

18 

10 
10 

3406.955 

3455-3«4 
3478.001 

424 
428 

431 

Fe 
Fe 
Fe 

4 

2 

4 

J4 

4073.920 
4088.716 
4114.600 

265 

Fe 
Co 

3 
5 

4 

IO 

3500.721 
3518.487 

434 
436 

Fe 
Fe 

3 
3 

17 

20 

4I57-948 
4185.063 

269 

Fe 

5 

10 

3540.266 

439 

Fe 

5 

4 

4202.188 

274 
278 

1    Fe    \ 
Fe 
Fe? 

Id? 
40 
4 

12 

6 

12 

3564.680 

358L344 
.3583.483 

^445 
448 

456 

Ca 
Cr 
Fe 

IO 

I 

4 

10 

15 

9 

4226.892 
4254.502 
4271.924 
4293-249 

284 

Fe 

4 

12 

3597-I92 

(  Ca 

2) 

3 

43O7.9O4 

290 

Fe 

15 

IO 

3609.015 

£462 

)     _ 

-  \d 

3 

4308.034 

292 

294 
298 

Fe 
Fe 
Fe 

4 

20 

4 

'5 
10 

14 

3612.217 
3618.924 
3623.332 

467 

\  Fe 
Fe 
Fe 

4 

3 

10 

'5 
17 

4308.071 
4325.940 
4352.903 

301 
307 

311 

Fe 
Fe 
Fe 

20 
IO 

3 

10 

II 

13 

3631.619 

3647-995 
3667.397 

473 
477 

Fe 
Fe 
Ca 

IO 

8 
4 

ii 
ii 

4383721 
4404.927 
4425.609 

3i3 

(  Co  ) 
Fe  ( 

/   Va  ) 

6 

'3 

3683.202 

480* 
484 

Fe 
Fe 

5 
5 

18 
18 

4447.899 
4494-735 

320 
324 

Fe 
Fe 

5 
5° 

II 

IO 

3707.186 
3720.086 

490 
493 

Ti 
Ba 

4 
7 

17 
8 

4508.456 
4554.213 

327 

Fe 

5 

15 

3732.542 

496 

Ti 

6 

J4 

4572.I57 

338 

Fe 

20 

8 

3789-633 

500 

Fe 

4 

20 

4602.183 

34i 

Fe 

15 

7 

3758-379 

505 

(   Ti    ) 
(   Co  \ 

5 

13 

4629.515 

348 

Fe 

3 

15 

3781.330 

508 

Fe 

4 

17 

4643.645 

i 

Fe 

Fe 

3 

30 

15 
4 

3804.153 
3820.567 

512 

Fe 

Ni 

6 

4 

12 

12 

4679.028 
4686.395 

361 

Fe 

20 

4 

3826.024 

5^§ 

Mg 

9 

II 

4703.180 

369 

Fe 

5 

8 

3843.406 

524 

Mn 

6 

I 

4783.601 

371 

Fe 

10 

3 

3860.048 

r^i 

Mn 

6 

12 

4823.697 

375 

C 

7 

3 

3883.472 

H 

15 

5 

4861.496 

S9 

Fe 

4 

12 

3897-599 

537 

Fe 

7 

4 

4919.183 

^387"* 

Ti 
Ca 

4 
300 

15 

5 

3924-669 
3933-809 

545 

(   Ti    ) 
i    Fe   \ 

3 

IO 

4973-274 

391 

Al 

10 

7 

3944.I59 

549 

Fe 

4 

7 

4994-3  i  6 

393 

Fe 

4 

15 

39SO.IOI 

558 

Ti 

3 

8 

5020.210 

397 
^399 

Fe 
Ca 

3 
200 

ii 

5 

3960.429 
3968.620 

561 
564 

Fe 
Fe 

5 
4 

12 
14 

5050.008 
5068.946 

404 

Fe,  Ti 

4 

3981.914 

567 

Fe 

2 

9 

5090.959 

*  This  line  is  doubly  reversed  and  spread  out  in  broad  shading  for  6.000  to  7.000  on  either  side.     In  each 

case  the  second  reversal  is  slightly  excentric  with  respect  to  the  other,  being  displaced  towards  the  red. 

t  Seven  or  eight  lines,  the  brightest,  and  most  of  the  others  are  due  to  iron. 

$  There  is  a  faint  side  line  towards  the  red. 

§  This  line  is  shaded  towards  the  violet,  probably  due  to  a  close  side  line. 

SMITHSONIAN  TABLES. 


173 


TABLE  1  79. 


STANDARD  WAVE-LENGTHS, 


No.  of 
Line. 

Element. 

Inten- 
sity and 
appear 
ance. 

Weight 

Wave- 
length (sun 
spectrum). 

No.  of 
Line. 

Element. 

Inten- 
sity and 
appear- 
ance. 

Weight. 

Wave- 
length (sun 
spectrum). 

570 

Fe 

2 

II 

5109.825 

762 

Fe 

6 

14 

5930.410 

575 

Fe 

4 

9 

5127.530 

764 

Si 

6 

H 

5948.761 

580 

Fe 

3 

5 

5141.916 

770 

Fe 

6 

7 

5987.286 

589 

Fe 

4 

13 

5162.448 

774 

Mn 

6 

6013.717 

778 

Fe 

6 

8 

6024.280 

(592 

Mg 

8) 

3 

5167.501 

^4  <  593 

- 

"I* 

7 

5l67-572 

782 

Fe 

7 

13 

6065.708 

(594 

Fe 

6) 

3 

5167.686 

786 

Ca 

6 

9 

6102.941 

(595 
fa  \  596 

Fe 

4) 

3 
5 

5169.066 
5169.161 

792 
797 

Ca 
Ca 

9 

IO 

ii 
9 

6122.428 
6162.383 

(  597 

Fe 

4) 

3 

5169.218 

804 

Fe 

8 

10 

6191.770 

*2|" 
£1601 

610 

Mg 
Mg 
Fe 

IO 

20 
4 

9 
ii 

IO 

5172.871 
5183-792 
521  5-352 

808 
811 
815 

Fe.Va 
Fe 
Fe 

7 
7 
5 

12 

9 
II 

6230.946 
6252.776 
6265.347 

614 

Fe 

8 

9 

5233-  !  24 

822 

Fe 

7 

7 

6301.719 

618 

Fe 

3 

12 

5253-649 

827 

Fe 

6 

12 

6335-550 

Ez  630* 

Fe 

8</? 

16 

5269.722 

834 

Fe 

7 

9 

6393.818 

EI  \  632 
(633 

Ca 
Fe 

;i' 

12 

5270.448 
5270.495 
5270.533 

838 

843 
846 

Fe 
Ca 
Ca 

7 
7 
5 

IO 

II 

7 

6411.864 
6439.298 
6471.881 

639 

Fe 

6 

II 

5283.803 

850 

Fe 

7 

9 

6495.209 

643 

Fe 

4 

IO 

5307.546 

856 

(Ti  I 
JFef 

6 

ii 

6546.486 

647 
655 

Fe 
Fe 

8 
6 

8 
8 

5324.373 
5367.670 

863 

H 
Fe 

30 

5 

ii 

6563.054 
6593.161 

659 

Fe 

6 

ii 

5383-576 

867 

Ni 

5 

IO 

6643.482 

662 

Fe 

7 

14 

5405.987 

870 

Fe 

5 

IO 

6678.232 

668 

Fe 

7 

9 

5347  -1  3° 

877 

Fe 

4 

12 

6750.412 

674 

Fe 

4 

10 

5463.493 

879 

Ni 

4 

n 

6768.044 

676 

Ni 

4 

10 

5477.128 

883 

Fe 

3 

8 

6810.519 

679 

Fe 

4 

8 

5501-685 

886 

Fe 

3 

6 

6441.591 

682 

Mg 

7 

8 

5528.636 

#896 

A(o) 

12 

6870.186 

687 

Fe 

s 

8 

5569.848 

911 

A(o} 

4 

T3 

6884.083 

690 

Ca 

6 

9 

5588.980 

925 

A(o) 

6 

9 

6909.675 

695 

Ca 

4 

4 

5601.501 

93  i 

A(o] 

4 

9 

6919.245 

699t 

Fe 

2 

12 

5624.253 

938 

A(wv) 

8 

IO 

6947.781 

7oot 

Fe,  Va 

4 

14 

5624.768 

940 

A(wv) 

8 

12 

6956.700 

706 

Fe 

5 

9 

5662.745 

957 

? 

6 

8 

7035-I59 

710 

Na 

6 

7 

5688.434 

961 

? 

6 

5 

7122.491 

717 

Fe 

5 

10 

5731-973 

969 

A(wv} 

10 

5 

7200.753 

720 

Fe 

5 

IO 

5753-342 

977 

A(wv} 

15 

4 

7243.904 

725 

CuPCo? 

Id? 

9 

5782.346 

984 

A(wv) 

IO 

3 

7290.714 

732 

Fe 

5 

7 

5806.954 

990 

p 

7 

2 

7389-696 

7371 

Ca 
He 

7 

L4 

5857-672 
5875.982 

99711 
998 

A(o) 
A(o) 

10 

4 
5 

7594-059 
7621.277 

/>2  743 

Na 

15 

20 

5890.182 

1004 

A(o) 

14 

3 

7660.778 

£>i745 

Na 

IO 

20 

5896.154 

IOIO 

4 

7714-686 

*  Component  about  .088  apart  on  the  photographic  plate.     It  is  an  exceedingly  difficult  double. 

t  Lines  used  by  Pierce  in  the  determination  of  absolute  wave-lengths. 

t  There  is  a  nickel  line  near  to  the  red. 

§  This  value  of  the  wave-length  is  the  result  of  three  series  of  measurements  with  a  grating  of  20,000  lines 

to  the  inch  and  is  accurate  to  perhaps  .02. 

||  Beginning  at  the  head  of  A  ,  outside  edge. 

SMITHSONIAN  TABLES. 


174 


TABLE  180. 


WAVE-LENGTHS   OF    FRAUNHOFER    LINES. 


For  convenience  of  reference  the  values  of  the  wave-lengths  corresponding  to  the  Fraunhofer  lines  usually  designated 
by  the  letters  in  the  column  headed  "  index  letters,"  are  here  tabulated  separately.  The  values  are  in  ten  mil- 
lionths  of  a  millimetre  on  the  supposition  that  the  D  line  value  is  5896.156.  The  table  is  for  the  most  part  taken 
from  Rowland's  table  of  standard  wave-lengths,  but  when  no  corresponding  wave-length  is  there  given,  the  number 
given  by  Kayser  and  Runge  has  been  taken.  These  latter  are  to  two  places  of  decimals. 


Index  letter. 

Line  due  to  — 

Wave-length  in 
centimetres  X  io8. 

Index  letter. 

Line  due  to  — 

Wave-length  in 
centimetres  X  10*. 

A 

i° 

t-b 

7621.277* 
7594-059* 

G'  or  Hy 

H 

fFe 

4340.66  § 
4308.071 

a 

- 

7184.781 

G 

- 

4308.034 

B 

0 

6870.l86t 

[ca 

4307.904 

C  or  Ha 

H 

6563-054 

g 

Ca 

4226.892 

a 

O 

6278.289! 

hor  H5 

H 

4101.87 

Di 

Na 

5896.154 

H 

Ca 

3968.620 

D2 

Na 

5890.182 

K 

Ca 

3933-809 

D3 

He 

5875-982 

L 

Fe 

3820.567 

fFe 

5270.533 

M 

Fe 

3727-763 

Ei 

- 

5270.495 

N 

Fe 

358I-344 

U. 

5270.448 

.       O 

Fe 

344I-I35 

E2 

Fe 

5269.722 

P 

Fe 

336I-30 

bi 

Mg 

5183.792 

Q 

Fe 

3286.87 

b2 

Mg 

fFe 

5172.871 
5169.218 

Rll 

Ca 
Ca 

3181.40 

3!79-45 

bs 

- 

5169.161 

v1F 

Fe 

3M4-S8  (?) 

b4 

IFe 
Fe 

5169.066 
5167.686 

5l67-572 

Si 
S2 

Fe 
-  Fe 
Fe 

3100.779 
3100.415 
3100.064 

Mg 

5167.501 

s 

Fe 

3047.720 

For  H0 

H 

4861.496 

T 

Fe 

3020.759 

d 

Fe 

4383-721 

t 

Fe 

2994.542 

f 

Fe 

4325-940 

U 

Fe 

2947-993 

*  The  two  lines  here  given  for  A  are  stated  by  Rowland  to  be  :  the  first,  a  line  "  beginning  at  the  head  of  A,  out- 
side edge;  "  the  second,  a  "  single  line  beginning  at  the  tail  of  A." 

t  The  principal  line  in  the  head  of  B. 

J  Chief  line  in  the  a  group. 

§  Ames,  "  Phil.  Mag."  (5)  vol.  30. 

||  Cornu  gives  3179.8,  which,  allowing  for  the  different  value  of  the  standard  D  line,  corresponds  to  about  3180.3. 

1  Cornu  gives  3144.7,  which  would  correspond  to  about  3145-2- 
SMITHSONIAN  TABLES. 

175 


TABLE  181. 

DETERMINATIONS    OF    THE    VELOCITY    OF    LIGHT,    BY    DIFFERENT 

OBSERVERS.* 


Wt.  of 

obser- 

Date of 
determi- 
nation. 

No.  of 
experi- 
ments 
made. 

Method. 

Interval 
worked 
across  in 
kilometres. 

Velocity  in 
kilometres  per 
second. 

Velocity  in  miles 
per  second. 

Refer- 
ence. 

vation 
as  esti- 
mated 
by 

Hark- 

ness. 

1849 

- 

Toothed  wheel 

8.633 

3'5324 

195935 

I 

O 

1862 

80 

Revolving  mirror 

0.02 

298574  ±  204 

l85527=l=I27 

2 

I 

1872 

658 

Toothed  wheel 

10.310 

298500  J-  995 

l8548l    ;±-6l8 

3 

I 

I874 

546 

«            « 

22.91 

300400^300 

186662  -J-  186 

4 

2 

1879 

100 

Revolving  mirror 

0.6054 

299910^51 

186357  i  3i-7 

5 

3 

1880 

12 

Toothed  wheel 

|  5-I3I3  I 
I  5-5510  J 

301384-1-263 

187273  ±'64 

6 

I 

,     f 

148 

Revolving  mirror 

5.IOI9 

299709 

186232 

7 

_ 

1880 

to  \ 
1882 

39 

<«            « 

7.4424 

299776 

186274 

7 

- 

I 

65 

"            u 

7.4424 

299860 

186326 

7 

6 

1882 

23 

«            « 

0.6246 

299853±6o 

186322-1-37 

8 

3 

Mean  from  all  weighted  measurements    .     . 

299835=1=154 

186310^-95.6 

9 

Mean  from  those  having  weights  >  I   .     .    . 

299893  =1=  23 

186347  ^  14.3 

9 

i  Fizeau,  "  Comptes  Rendus,"  1849. 

2  Foucault,  "  Recueil  des  travaux  scientifiques,"  Paris,  1878. 
3  Cornu,  "  Jour,  de  1'Ecole  Polytechnique,"  Paris,  1874. 

4  Cornu,  "  Annales  de  1'Observatoire  de  Paris,"  Memoires,  tome  13,  p.  A.  298,  1876. 

5  Michelson,  "  Proc.  A.  A.  A.  S."  1878. 

6  Young  and  G.  Forbes,  "  Phil.  Trans."  1882. 

7  Newcomb,  "Astronomical  Papers  of  the  American  Ephemeris,"  vol.  2,  pp.  194,  201,  and  202. 
8  Michelson,  "  Astronomical  Papers  of  the  American  Ephemeris,"  vol.  2,  p.  244. 

9  Harkness. 

TABLE  182. 


PHOTOMETRIC   STANDARDS.t 


Name  of  standard. 

Violle 
units. 

Carcels. 

Star 
candles. 

German 
candles. 

English 
candles. 

Hefner- 
Alteneck 
lamps. 

Violle  units  J     . 

I.OOO 

2.08 

16.1 

16.4 

I8.5 

18.9 

Carcels      

0.481 

I.OO 

7-75 

7.89 

8.91 

9.08 

Star  candles      .... 

0.062 

0.130 

I.OO 

1.02 

!-'5 

I.I7 

German  candles 

0.061 

0.127 

0.984 

I.OO 

L'3 

1-15 

English  candles 

0.054 

O.II2 

0.870 

0.886 

I.OO 

1.02 

Hefner-Alteneck  lamps     . 

0-053 

O.II4 

0.853 

0.869 

0.98 

I.OO 

*  Quoted  from  Harkness,  "  Solar  Parallax,"  p.  33. 

t  This  table,  founded  on  Violle's  experiments,  is  quoted  from  Paterson's  translation  of  Palaz'  "  Industrial  Pho- 
tometry,'' p.  '73. 

$  The  Violle  unit  is  sometimes  called  the  absolute  standard  of  white  light.  It  is  the  quantity  of  light  emitted 
normally  by  one  square  centimetre  of  the  surface  of  melted  platinum  at  the  temperature  of  solidification. 

SMITHSONIAN  TABLES. 

176 


TABLE  183. 


SOLAR    ENERGY  AND  ITS   ABSORPTION    BY  THE    EARTH  ATMOSPHERE. 


This  table  gives  some  of  the  results  of  Langley's  researches  on  the  atmospheric  absorption  of  solar  energy.*  The 
first  column  gives  the  wave-length  A,  in  microns,  of  the  spectrum  line,  while  the  second  and  third  columns  give 
the  corresponding  absorption,  according  to  an  arbitrary  scale,  for  high  and  low  solar  attitudes.  The  fourth  column, 
E,  gives  the  relative  values  of  the  energy  for  the  different  wave-lengths  which  would  be  observed  were  there  no 
terrestrial  atmosphere. 


A 

«1 

a. 

E 

0*-375 

112 

27 

353 

400 

235 

63 

683 

•45° 

424 

140 

1031 

.500 

570 

225 

1203 

.600 

621 

311 

1083 

.700 
.800 

553 

372 

324 
246 

849 
5X9 

.900 

238 

167 

3i6 

1.  000 

235 

167 

309 

TABLE  184. 


THE   SOLAR   CONSTANT. 


The  "  solar  constant  "  is  the  amount  of  heat  per  unit  of  area  of  normally  exposed  surface  which,  at  the  earth's  mean 
distance,  would  be  received  from  the  sun's  radiation  if  there  were  no  terrestrial  atmosphere.  The  following  table 
is  taken  from  Langley's  researches  on  the  energy  of  solar  radiation. t  The  first  column  gives  the  wave-length  in 
microns.  The  second  and  third  columns  give  relatively  on  an  arbitrary  scale  a  >  upper  and  a  lower  limit  to  the 
possible  value  of  spectrum  energy. 


Spectrum 

Spectrum 

Spectrum 

Spectrum 

Wave- 
length. 

energy 
(upper 
limit). 

energy 
(lower 
limit). 

Wave- 
length. 

energy 
(upper 
limit). 

energy 
(lower 
limit). 

0^.530 

•375 

203-9 
196.6 

122.5 
IIO.O 

I^.OOO 
I.2OO 

105.0 

78.2 

IO2-3 
61.3 

.400 

242.2 

I39-1 

1.400 

65.I 

•  5^.2 

•45° 

783.2 

I05-5 

1.  600 

48.0 

45-° 

.500 

852.9 

374-1 

1.  800 

39-2 

36-4 

.600 

5'4-7 

333-° 

2.OOO 

29.1 

27.1 

.700 

317.7 

255-4 

2.2OO 

19.4 

17-5 

.800 

173-9 

167.3 

2.4OO 

7.0 

6.8 

The  areas  of  the  energy  curves  are  respectively 
The  solar  constants  deduced  from  these  areas  are 


149,060  and  95,933 
3.505  and    2.630 


Langley  concludes  that  "in  view  of  the  large  limit  of  error  we  can  adopt  three  calories  as  the  most  probable  value 
of  the  solar  constant,"  or  that  "  at  the  earth's  mean  distance,  in  the  absence  of  its  absorbing  atmosphere,  the  solar 
rays  would  raise  one  gramme  of  water  three  degrees  per  minute,  for  each  normally  exposed  square  centimetre  of  its 
surface." 

*  "Am.  Jour,  of  Sci."  vols.  xxv.,  xxvii.,  and  xxxii. 

t  "Professional  Papers  of  U.  S.  Signal  Service,"  No.  15,  1884. 


SMITHSONIAN  TABLES. 


177 


TABLE  185. 


INDEX   OF   REFRACTION    FOR   CLASS. 


The  table  gives  the  indices  of  refraction  for  the  Fraunhofer  lines  indicated  in  the  first  column.  The  kind  of  glass, 
the  density,  and,  where  known,  the  corresponding  temperature  of  the  glass  are  indicated  at  the  top  of  the  different 
columns.  When  the  temperature  is  not  given,  average  atmospheric  temperature  may  be  assumed. 


(a)  FRAUNHOFER'S 

DETERMINATIONS. 

(Ber.  Munch.  Akad.  Bd.  5. 

Flint  glass. 

Crown  glass. 

Density     = 
Temp.  G.  = 

3-723 

3-5" 

2-756 

i7"s 

2-535 

B 

1.62775 

I. 

60204 

I. 

55477 

1.52 

S83 

I-52431 

C 

.62965 

.60380 

55593 

•52 

685 

.52530 

D 

.63504 

.60849 

.55908 

•52959 

.52798 

E 

.64202 

•61453 

5631  5 

•53301 

•53r37 

F 

.64826 

.62004 

56674 

•53605 

•53434 

G 

.66029 

.63077 

57354 

.54166 

•53991 

H 

.67106 

.64037 

57947 

•54657 

•54468 

(b)  BAILLE'S  DETERMINATIONS.     (Quoted  from  the  Ann.  du  Bur.  des  Long.  193,  p.  620.) 

Flint  glass. 

Density     — 

2.98 

3-22 

3-24 

3-44 

3-54 

3.63 

3-68 

4.08 

5-oo 

Temp.  C.  = 

22°.0 

23°-2 

U°.7 

24°.0 

B 
C 

1.5609 
-5624 

I-5659 

•5675 

1.5766 
•5783 

I 

.5966 
.S982 

I.< 
.< 

3045     i 
3062 

.6131 
.6149 

1.6237 
.6255 

1.6771 
.6795 

1.7801 
.7831 

D 
bi 
F 

.5660 

•5715 
.5748 

•5715 
•5776 
•5813 

.5822 
.5887 
•5924 

.6027 
.6098 
.6141 

.6109 
.6183 
.6225 

.6198 
.6275 
•6321 

.6304 

.6384 

.6429 

.6858 

.6959 
.7019 

.7920 
.8062 
.8149 

G 

.5828 

.5902 

>I8 

.6246 

.( 

333  5 

•6435 

.6549 

.7171 

.8368 

II 

.5898 

•5979 

.6098 

•6338 

.6428 

•6534 

.6647 

•73°6 

.8567 

Crpwn  glass.     (Bailie,  ibid.) 

Density     = 

2.49 

2.50 

2-55 

2.80 

3-oo 

Temp.  C.  = 

23°-S 

I7-.8 

i8°.4 

2I°.2 

2I°.9 

B 

I.5I2 

3 

I 

5244 

I 

5226 

I.5l 

S7 

I-SSS4 

C 
D 

•5134 
.5160 

5280 

•5237 
.5265 

.5166 
.5192 

.5568 
•5604 

bi 

.5198 

5320 

5307 

•5234 

.5658 

F 

.5222 

5343 

5332 

.5256 

.5690 

G 

.5278 

5397 

5392 

•53'3 

•5769 

H 

•5323 

5443 

5442 

;6o 

.5836 

(c)  HOPKINSON'S  DETERMINATIONS. 

(Proc.  Roy.  Soc. 

vol.  26.) 

Ward 

Soft 

Titani- 

crown. 

crown. 

silicic 
crown. 

Flint  glass. 

Density  = 

2.486 

2-55° 

2-553 

2.866 

3.206 

3-659 

3.889 

4.422 

A 

I.5U75S 

1.508956 

_. 

1.534067 

_ 

i  .6391  43 

1.696531 

B 
C 

:55l4568 

.510916 
.511904 

I-539I55 

.540255 

.536450 
•537673 

1.56855 
.57001 

8    1.615701 
i     .617484 

.642874 
.644866 

.701060 

.703478 

D 
E 
bi 
F 
(G) 
G 
h 

.517114 

•520331 
.520967 

•523J39 
.527994 
•528353 
•530902 
•532792 

•5H591 
.518010 
.518686 
.520996 
.526207 
•526595 
•529359 

•543249 
.547088 

•547852 
•550471 
•556386 
.556830 
•559999 
•562392 

.54101  1 
.545306 
.546166 
.549121 
•555863 
•556372 
.560010 
.562760 

•57401 

.57922 
.58027 
.5838S 
•592K 

.5928: 

•5973: 
.6007: 

5     -622414 
3     -628895 
i     .630204 
61    -634748 
>o     .645267 
4      .646068 

2        .651840 

7      .656219 

.650388 

•657653 
.659122 
.664226 
.676111 
.677019 
•683577 
.688569 

.710201 
.719114 
.720924 
.727237 
.742063 

•743204 
.751464 

.757785 

N.  B.  —  D  is  the  more  refrangible  of  the 

pair  of  sodium  lines  ; 

(G)  is  the  hydrogen  line  near  G. 

SMITHSONIAN  TABLES. 


178 


INDEX    OF    REFRACTION    FOR    CLASS. 


TABLE  185. 


(d)  MASCART'S  DETERMINATIONS.   (Ann.  Chim.  Phys. 

(e)  LANGLEY'S  DETERMINATIONS.     (Silliman's  Jour- 

nal, 27,  1884.) 

Flint  glass. 

Crown  glass. 

Flint  glass. 

Density  = 

3-615 

3-239 

2.578 

Wave  length 

Index  of 

Temp.    = 

30-.  o 

26u.O 

in  mm.  X  io6. 

refraction. 

A 
B 

1.60927 
.61268 

1.57829 
.58114 

1.52814 
•530II 

2030 
1918 

I-55I5 
.5520 

1870 

•5535 

C 

.61443 

.58261 

53"3 

1810 

•5544 

D 

.61929 

.58671 

53386 

1580 

•5572 

1540 

•5576 

E 

.62569 

•59*97 

53735 

1360 

.5604 

b4 

.62706 

•59304 

53801 

1270 

.5616 

II3C 

> 

•5636 

F 

.63148 

.59673 

54037 

940 

.5668 

G 

.64269 

.60589 

54607 

9IO 

.56/4 

89C 

> 

•5678 

H 

.65268 

.61390 

55093 

850 

•5687 

L 

.65817 

.62012 

•55349 

815 

•5697 

760.1  = 

=  A 

•5714 

M 

.66211 

.62138 

. 

55531 

656.2  = 

=  C 

•5757 

N 

.66921 

.62707 

55853 

588.9  = 

=  DI 

•5798 

516.7  = 

=  b4 

.5862 

O 

.67733 

•63341 

. 

56198 

486.1  = 

=  F 

•5899 

P 

•63754 

. 

56419 

396.8  = 

-  HI 

.6070 

Q 

~ 

.64174 

56646 

344.0  =  O 

.6266 

(f)  EFFECT  OF 

TEMPERATURE.    (Vogel,  Wied.  Ann. 

vol.  25.) 

where  nt  is  the  absolute  index  of  refraction  for 

the 

temperature  t,  and  a  and  B  are  constants.     For  tem- 

peratures rangi 

ng  from  12°  to  260°  Vogel  obtains 

the 

following  value 

s  of  a  and  B  for  the  Fraunhofer  '. 

mes 

given  at  the  tops  of  the  columns. 

ffa        D         ffp 

JT, 

White  glass  j 

O.I08  = 

96      123      224 

107     106       97 

327 
93 

Flint  glass    j 

O.IO8  = 
)8.I01U= 

190     190     362 

IOI        147       221 

575 

221 

(g)  EFFECT  OF  TEMPERATURE. 

(Muller,  Publ.  d.  Astrophys.  Obs.  zu  Potsdam,  1885.) 

'Flint  glass. 

Crown  glass. 

hofer 
line.                    Density  =  3.855. 
Temp.  C.  =—  i  °  to  24°. 

Density  =  3.  218. 
Temp.C.  =  —  3°  to  21°. 

Density  =2.522. 
Temp.  C.  =  —  5°  to  23°. 

B            1-643776  +  .00000474  1 
C             -645745  +  .00000486  1 
D             .651193+  .00000495  / 
bi             .6^9632  +  .000007102* 
F             -664936  +  .00000653  t 

Hy                    .676720  +  .00000783  t 
h                       .684144+  .00000861  t 

i  -574359  +  .  00000324  * 
.575828+  .00000333  1 
.5798  56+.  00000323  f 
.586000  +  .00000443  / 
.589828  +  -00000439  / 
.598205  +  .00000560  1 
•603398  +  .00000636  / 

1.512588  —  .OOOOOO43  t 

•51  3558  —  -00000033  / 

.516149  +  .OOOOOOI7  / 
.520004  +  .OOOOOO54  t 
.522349  +  .00000048  / 
.527360  +  .00000082  / 
.520376+  .00000143  t 

N.  B.  —  The  above  examples  on  the  effect  of  temperature  give  an  idea  of 
effect,  but  are  only  applicable  to  the  particular  specimens  experimented  on. 

the  order  of  magnitude  of  that 

SMITHSONIAN   TABLES. 


179 


TABLE  186. 


INDEX    OF   REFRACTION. 

Indices  of  Refraction  for  the  various  Alums.* 


t 

o 
U 

Index  of  refraction  for  the  Fraunhofer  lines. 

1 

1 

a 

B 

c 

D 

E 

b 

F 

G 

Aluminium  Alums,     .ff  Al(SO4)2-f-i2H2O.t 

Na 

1.667 

17-28 

1.43492 

143563 

1  43653 

1.43884 

1.44185 

1.44231 

1.44412 

1.44804 

NH3(CH3) 

1.568 

7-17 

45OI3 

.45062 

45177 

.45410 

.45691 

45749 

.45941 

46363 

K 

1-735 

14-15 

.45226 

45303 

45398 

45645 

45934 

45996 

.46181 

.46609 

Rb 

1.852 

7-21 

45232 

45328 

454*7 

.45660 

45955 

45999 

.46192 

.46618 

Cs 
NH4 

1.961 
1.631 

15-25 

15-20 

45437 
45509 

455*7 
45599 

.45618 
45693 

45856 
45939 

.46141 
.46234 

.46203 
.46288 

.46386 
.46481 

.46821 
46923 

Te 

2.329 

10-23 

.49226 

49317 

49443 

.49748 

.50128 

.50209 

.50463 

.51076 

Indium  Alums.     /?In(SO4)24-i2H2O.t 

Rb 

2.06^ 

3-13 

1.45942 

1.46024 

1.46126 

1.46381 

1.46694 

1.46751 

146955 

1.49402 

Cs 

2.241 

17-22 

.46091 

.46170 

.46283 

.46522 

.46842 

.46897 

47*05 

47562 

NH4 

2.01  1 

17-21 

.46193 

46259 

46352 

.46636 

46953 

47015 

47234 

4775° 

Gallium  Alums.     .ffGa(SO4)2-f-i2H2O.t 

Cs 

2.II3 

17-22 

1.46047 

1.46146 

1.46243 

1.46495 

1.46785 

1.46841 

1.47034 

1.47481 

K 
Rb 

1.895 
1.962 

19-25 

.46118 
.46152 

.46195 
.46238 

.46296 

.46528 
46579 

.46842 
.46890 

.46904 
.46930 

47093 
.47126 

47548 
47581 

NH4 

1-777 

15-21 

4639° 

.46485 

46575 

.46835 

47*46 

.47204 

474*2 

.47864 

Te 

2.477 

1  8-20 

.50112 

.50228 

•50349 

.50665 

•5I057 

•5**3* 

•51387 

.52007 

Chrome  Alums.     .ffCr(SO4)2-f  i2H2O.f 

Cs 

2.043 

6-12 

1.47627 

147732 

1.47836 

1.48100 

1.48434 

1.48491 

1.48723 

1.49280 

K 
Rb 

1.817 
1.946 

6-17 

12-17 

.47642 
.47660 

4773s 
47756 

.47865 
.47868 

48137 
.48151 

.48459 
.48486 

485*3 
.48522 

48753 
48775 

493°9 
49323 

NH4 

1.719 

7-18 

.47911 

.48014 

48125 

.48418 

.48744 

.48794 

.49040 

49594 

Te 

2.386 

9-25 

.51692 

•5I798 

•5*923 

.52280 

.52704 

•52787 

.53082 

•53808 

Iron  Alums.     7?Fe(SO4)2+i2H2O.t 

K 

r.  806 

7-1  1 

1.47639 

1.47706 

147837 

1.48169 

1.48580 

1.48670 

1.48939 

1.49605 

Rb 

1.916 

7-20 

.47700 

47770 

47894 

48234 

48654 

.48712 

.49003 

.49700 

Cs 

2.061 

20-24 

47825 

.47921 

.48042 

.48378 

48797 

.48867 

.49136 

.49838 

NH4 

1.713 

7-20 

.47927 

.48029 

.48150 

.48482 

.48921 

48993 

.49286 

.49980 

Te 

2-385 

15-17 

•5*674 

•5*790 

•5*943 

•52365 

.52859 

•52946 

.53284 

.54112 

*  According  to  the  experiments  of  Soret  (Arch.  d.  Sc.  Phvs.  Nat.  Geneve,  1884.  1888,  and  Comptes  Rendus.  1885). 
t  R  stands  for  the  differei    '  '      '     "  ' 


SMITHSONIAN  TABLES. 


ferent  bases  given  in  the  first  column. 
1 80 


TABLE  187. 


INDEX  OF  REFRACTION. 

Index  of  Refraction  of  Metals  and  Metallic  Oxides. 


(a)   Experiments  of  Kundt  *  by  transmission  of  light  through  metallic  prisms  of  small  angle. 

Name  of  substance. 

Index  of  refraction  for 

Red. 

White. 

Blue. 

Silver 
Gold 
Copper      .        . 

• 

. 

0.38 

0.45 
1.76 

1.81 

2.17 

2.61 
1.04 
0.89 

1.78 
2.18 
2.63 

3-3i 
4.99 

0.27 
0.58 
0.65 
1.64 

i-73 

2.OI 
2.26 

0-99 
2.03 
I.9I 
2.1  1 

2.23 
2.84 

3-29 
4-82 

1.  00 

0-95 
1.44 

1.85 
2.13 
I-25 
i-33 

2.36 
2-39 
3-i8 
2.90 
4.40 

Nickel 

Bismuth    ....... 
Gold  and  gold  oxide                                   , 

""til!." 
Bismuth  oxide  
Iron  oxide          ...                 . 
Nickel  oxide      ...         ... 
Copper  oxide     
Platinum  and  platinum  oxide  . 

«                                                14                           « 

(to)  Experiments  of  Du  Bois  and  Rubens  by  transmission  of  light  through  prisms  of  small  angle. 

The  experiments  were  similar  to  those  of  Kundt,  and  were  made  with  the  same  spectrometer. 
Somewhat  greater  accuracy  is  claimed  for  these  results  on  account  of  some  improvements  intro- 
duced, mainly  by  Prof.  Kundt,  into  the  method  of  experiment.     There  still  remains,  however, 
a  somewhat  large  chance  of  error. 

Name  of  metal. 

Index  of  refraction  for  light  of  the  following  color  and  wave-length. 

Red(Lia).            "Red." 
A  =  67.1              A  =  64.4 

Yellow  (D). 
A  -58.9 

Blue  (F). 
A  =  48.6 

Violet  (G). 
A  =  43.1* 

Nickel     . 
Iron 
Cobalt     . 

2.04 
3.12 
3.22 

'•93 
3.06 
3.10 

1.84 
2.72 
2.76 

I.7I 

2-43 
.       2.39 

1-54 
2.05 
2.IO 

(C)   Experiments  of  Drude. 

The  following  table  gives  the  results  of  some  of  Drude's  experiments.  §    The  index  of  refrac- 
tion is  derived  in  this  case  from  the  constants  of  elliptic  polarization  by  reflection,  and  are  for 
sodium  light. 

Metal. 

Index  of                                  Mptal 
refraction. 

Index  of 
refraction. 

Aluminium 
Antimony 
Bismuth            .         . 
Cadmium 
Copper    .... 
Gold        .... 
Iron          .... 
Lead        .... 
Magnesium 

1.44             Mercury 
3.04             Nickel     .... 
1.90             Platinum 
1.13             Silver       .... 
0.641            Steel        .... 
0.366           Tin,  solid 
2.36               "     fluid 
2.01             Zinc         .... 
o-37 

i-73 
1.79 
2.06 
0.181 
2.41 
1.48 

2.IO 
2.12 

*  "  Wied.  Ann."  vol. 
$  Wave-lengths  A  are 

34,  and  "  Phil    Mag."  (5)  vol.  26.                            t  Nearly  pure  oxide, 
in  millionths  of  a  centimetre.                                    §  "  Wied.  Ann."  vol.  39. 

SMITHSONIAN  TABLES. 


181 


TABLES  188,  189, 


INDEX   OF   REFRACTION. 

TABLE  188.  —Index  of  Refraction  of  Rock  Salt 


Determined  by  Langley. 
Temp.  24°  C. 

Determined  by  Rubens  and 
Snow. 

Determined  by  other  authorities. 

Line  of 
spec- 
trum. 

Wave- 
length 
in  cms. 
X  io6. 

Index  of 
refraction. 

Line  of 
spec- 
trum. 

Wave- 
length 
in  oiis. 
X  io6. 

Index  of 
refrac- 
tion. 

Line  of 
spec- 
trum. 

Index  of 
refraction. 

Authority. 

M 

37.27 

1.57486 

Hy 

43-4 

1.5607 

Ha 

1.54046 

j 

L 
H2 

38.20 

39-33 

•57207 
.56920 

F 
D 

48.5 
58.9 

•5531 
.5441 

Hy 

.56056 

>  Haagen  at  20°  C. 

HI 

39-68 

.56833 

C 

65.6 

.5404 

G 
F 

43-03 
48.61 

.56133 

.55323 

75-5 
79.0 

•5370 
•5358 

Ha 
H/3 

1.54095 
.55384 

)  Bedson  and 
>  Carleton  Williams 

b4 

51.67 

•54991 

83-1 

•5347 

Hy 

•525I5 

)atiS°C. 

bi 

5I-83 

•54975 

87.6 

•5337 

DI 

57.89 

.54418 

92-3 

•5329 

B 

1.53884 

D2 

58.95 

•544M 

97-8 

•532  i 

C 

.54016 

C 

65.62 

•54051 

103-5 

•5313 

D 

.54381 

•  Miilheims. 

B 

68.67 

•539*9 

110.7 

•53°5 

E 

.54866 

A 

76.01 

•5367 

118.6 

•5299 

F 

.55280 

p<rr 

94- 

•5328 

127.7 

.5293 

"3- 

•5305 

138.4 

.5286 

A 

1-53663 

"V 

139. 

•5287 

151.1 

.5280 

Bj 

n 

132. 

.5268 

166.0 

•5275 

< 

•53902 

184.5 

.5270 

C    \ 

•54050 

Determined  by  Baden  Powell. 

207.6 

237.2 

•5264 

.5257 

\ 
1 

•54032 
.54418 

Stefan  at  17°  and 
22°  C.    The  up- 

277.1 

.5247 

1 

•54400 

302.2 

.5239 

E 

.54901 

per  values  are 
at  17°  and  the 

~ 

1-5403 

332.0 

•5230 

( 

.54882 

lower  at  22°  for 

C 
D 

_ 

-54I5 
.5448 

369-0 
415.0 

•5217 
.5208 

F! 

.55324 
.55304 

each  line. 

E 

— 

.5498 

474-5 

•5r97 

G  i 

.56129 

F 

- 

•5541 

554-o 

.5184 

G  1 

.56108 

G 

— 

.5622 

644.7 

•5l63 

TT     J 

.56823 

H 

.5691 

830-7 

.5138 

1 

.56806 

TABLE  189. —Index  of  Refraction  of  Sylvine  (Potassium  Chloride). 


Determined  by  Rubens  and  Snow. 

Determined  by  other  authorities. 

Wave-length 
in  cms.  X  io". 

Index  of 
refraction. 

Wave- 
length  in 
cms.  X  io6. 

Index  of 
refraction. 

Line  of 
spec- 
trum. 

Index  of 
refraction. 

Authority. 

43-4  (Hy) 

1.5048 

145.8 

1.4766 

A 

1.48377 

48.6  (F) 

.4981 

160.3 

476l 

B 

.48597 

58-9  (D) 

.4900 

I78.I 

•4755 

C 

•48713 

65.6  (C) 

.4868 

200-5 

•4749 

D 

.49031 

k  Stefan  at  20  C. 

E 

•49455 

80.2 

1.4829 

229.1 

1.4742 

F 

.49830 

84-5 

.4819 

267-3 

4732 

G 

.50542 

89-3 

.4809 

320.9 

.4722 

H 

.51061 

94-4 

.4807 

356.I 

4717 

B 

-4754 

C 

.4767 

100.3 
107.0 

14795 
.4789 

400.1 

457-7 

1.4712 
.4708 

D 
E 

.4825 
.4877 

^Grailich. 

II4-5 
123.4 

.4781 
.4776 

534-5 
641.2 

.4701 
.4693 

F 
G 

•4903 
•5°°5 

D 

.4904 

Tschermak. 

1337 

1.4771 

802.2 

1.4681 

D 

•4930 

Groth. 

SMITHSONIAN  TABLES. 


182 


TABLE  190. 


INDEX   OF   REFRACTION. 

Index  of  Refraction  of  Fluor-Spar. 


Determined  by 
Rubens  and  Snow. 

Determined  by 
Sarasin. 

Determined  by  the 
authorities  quoted. 

Wave-length 
in  cms. 
X  10°. 

Index 
of 
refraction. 

Line 
of 
spectrum. 

Wave- 
length in 
cms.  X  io6. 

Index 
of 
refraction. 

Line 
of 
spectrum. 

Index 
of 
refraction. 

Authority. 

434(Hy) 

1-4393 

A 

76.040 

I.43IOIO 

D 

14339 

Fizeau. 

48-5(F) 

4372 

a 

71.836 

43  *  57  5 

58-9(0) 

4340 

B 

68.671 

•43  i  997 

A 

1.43003 

65.6(C) 

4325 

c 

65.618 

432571 

a 

43I53 

80.7 

•43°7 

D 

58.920 

433937 

B 

.43200 

85.0 

•4303 

F 

48.607 

•437051 

c 

43250 

Mulheims. 

89.6 

.4299 

h 

4I.OI2 

.441215 

D 

43384 

95-o 

4294 

H 

39.681 

442137 

E 

43551 

100.9 

.4290 

Cd 

36.090 

.445356 

F 

.43696 

107.6 

.4286 

" 

34-655 

.446970 

115.2 

.4281 

« 

34-015 

447754 

B 

1.43200 

124.0 

4277 

« 

32-525 

.449871 

D 

4339° 

134-5 

.4272 

« 

27.467 

459576 

F 

43709  • 

Stefan. 

146.6 

.4267 

« 

25-7I3 

.464760 

G 

.43982 

161.3 

.4260 

" 

23-I25 

.475166 

H 

.44204 

179.2 

.4250 

a 

22.645 

.477622 

201.9 

.4240 

« 

21-935 

48I51  5 

Red 

1-433     ) 

DesCloi- 

230-3 

.4224 

« 

21.441 

.484631 

Yellow 

•435     1 

seaux. 

268.9 

.4205 

Zn 

20.988 

487655 

322.5 
403-5 

.4174 
.4117 

H 

20.610 
20.243 

.490406 
493256 

Na 
u 

1.4324*) 

4342t  ) 

Kohl- 

rausch. 

462.0 

.4080 

Al 

19.881 

.496291 

538-o 

.4030 

« 

19.310 

.502054 

646.0 

.3960 

« 

18.560 

•509404 

807.0 

_____ 

.3780 

•^^••••••B 

••§••••••• 

••••^••^•H 

•^M^B^Hi^BHi 

KB^^MHHBBB 

•••IHI^HHHH 

••^•••••••••••iB^^H 

*  Gray  at  23°  C. 
f  Black  at  19°  C. 


SMITHSONIAN  TABLES. 


183 


TABLE  191. 


INDEX   OF   REFRACTION. 

Various  Monorefringent  or  Optically  Isotropic  Solids. 


Substance. 

Line  of 
Spectrum. 

Index  of 
Refraction. 

Authority. 

Agate  (light  color)      
Ammonium  chloride  

red 
D 
D 

1-5374 
1.6422 

I.7CC 

De  Senarmont. 
Grailich. 
DesCloiseaux. 

D 

/  JJ 

I.  ">7l6 

Fock. 

Bell  metal           

D 

1.0052 

Beer 

Blende         .                 

(Li 

?Na 

2.34165  ) 

2.-?6Q21  > 

Ramsay. 

(Tl 
(C 
<D 

2.40069  ) 
1.46245) 
1.46^0'?  1 

(F 
(C 
?D 

1.47024  1 
I.5I222  f 
1.51484 

Bedson  and 
Carleton  Williams. 

(  F 
D 

1.52068] 
\  I>53A 

Kohlrausch. 

(red 

(  L5462 

2.414    ; 

Mulheims. 
DesCloiseaux. 

|  green 
(B 

)D 

2.428    f 
2.46062  ) 
2.46086  > 

Schrauf 

fg 

2.47902  ) 

1.6 

Ayrton  &  Perry. 

I* 

j  C 

i-73       1 
1.81 
i.qo        \- 

\Vernicke. 

Garnet  (different  varieties) 

G 

IH 

D 

red 

I-3I 

!-54       j 
{  1-74  to  / 
}  1.90        f 
1.4.80 

Various. 
Tamin. 

D 

i-5H 
1.4061 

Wollaston. 
Tschichatscheff. 

D 

J<739 

Levy  &  Lecroix. 

D 

(  1.48210? 

Various. 

Opal    . 

D 

]  1.486      J 
1.406      { 

Pitch  
Potassium  bromide     
"           chlorstannate    .... 
"          iodide         

red 
D 

I  1-450      J 
I-53I 
1-5593    ) 
1-65/4    > 
1.6666    ) 

Wollaston. 

Topsoe  and 
Christiansen. 

« 

2.1442 

Gladstone  &  Dale. 

Resins  :  Aloes    
Canada  balsam     .... 

red 

H 

1.619 
1.528 
I.W8 

Jamin. 
Wollaston. 
Jamin. 

Copal    
Mastic  
Peru  balsam          .         . 

a 
II 

D 
'A 
B 

!:iS 

!-535 
1-593 

2-653     I 

2.730 

Wollaston. 
Baden  Powell. 

Sirks. 

'  C 
D 
D 

2.86 
2.98       J 

2.C71          ) 

Silver  <  chloride  
(  iodide     

SodaHckaeriike  wate/        \        \        \ 
Sodium  chlorate          
Spinel          
Strontium  nitrate         

< 
< 
i 

2.061 
2.182         ) 
1.4827       ) 
1.4833      ( 

i-S1^ 

J-7^55 
1.5667 

Wernicke. 

Feusner. 

Dussaud. 
DesCloiseaux. 
Fock. 

SMITHSONIAN   TABLES. 


184 


TABLE  192. 
INDEX  OF  REFRACTION. 

Index  of  Refraction  of  Iceland  Spar. 

jThe  determinations  of  Carvallo,  Mascart,  and  Sarasin  cover  a  considerable  range  of  wave-length,  and  are  here  given. 
Many  other  determinations  have  been  made,  but  they  differ  very  Tittle  from  those  quoted. 


Line  of 
spectrum. 

Wave- 
engih  in 
cms.  X  io6. 

Index  of  refraction  for  — 

Line  of 
spectrum. 

Wave- 
length in 
cms.  X  io8. 

Index  of  refraction  for  — 

Ordinary 
ray. 

Extraordi- 
nary ray. 

Ordinary 
ray. 

Extraordi- 
nary ray. 

Authority:  Carvallo. 

Authority  :  Sarasin. 

- 

215 

- 

1-4753 

Cd12 

32.53 

1.70740 

i.50857 

- 

198 

1.6279 

- 

Cd17 

27.46 

•741  51 

.52276 

- 

177 

- 

.4766 

Cd18 

25-71 

.76050 

•53019 

- 

154 

•6350 

- 

Cd23 

23.12 

.80248 

•54559 

- 

H5 

.6361 

•4779 

Cd24 

22.64 

.81300 

.54920 

- 

122 

.6403 

- 

Cd25 

21.93 

.83090 

•555M 

A 
B 

108 

76.04 
68.67 

.6424 
.65006 
•65293 

•44799 
.48275 
.48406 

Cd26 

21.43 

.84580 

•55993 

Authority  :  Mascart. 

A 
a 
B 

— 

1.65013 
.65162 
.65296 

1.48285 
.48409 

Authority:  Sarasin. 

A 

76.04 

1.65000 

1.48261 

a 

71.84 

•65156 

•48336 

C 

- 

.65446 

.48474 

B 

68.67 

.65285 

.48391 

D 

- 

.65846 

.48654 

Cds 

64-37 

.65501 

.48481 

E 

- 

•66354 

.48885 

D 

58.92 

•65839 

.48644 

b4 

- 

.66446 

- 

Cd2 

53-77 

.66234 

.48815 

F 

- 

.66793 

.49084 

Cd3 

53-36 

.66274 

.48843 

G 

- 

.67620 

.49470 

Cd4 

50.84 

•66525 

•48953 

H 

- 

.68330 

•49777 

F 

48.61 

.66783 

49079 

L 

- 

.68706 

.49941 

Cd5 

47-99 

.66858 

.49112 

M 

- 

.68966 

•50054 

Cd6 

46.76 

.67023 

.49185 

N 

- 

.69441 

.50256 

Cd7 

44.14 

.67417 

•49367 

O 

- 

•69955 

.50486 

h 

41.01 

.68036 

.49636 

P 

- 

.70276 

.50628 

H 

39-68 

.68319 

•49774 

Q 

- 

.70613 

.50780 

Cd9 

36.09 

•69325 

.50228 

R 

- 

•7H55 

.51028 

Cd10 

34-65 

.69842 

.50452 

S 

- 

.71580 

- 

Cdn 

34-oi 

.70079 

.50559 

T 

~ 

•71939 

SMITHSONIAN  TABLES. 


185 


TABLE   193. 


INDEX  OF  REFRACTION, 

Index  of  Refraction  ol  Quartz. 


Line  or  wave- 
length in  cms. 
X  io6. 

Index  for  — 

Line 
of 
spectrum. 

Index  for  — 

Ordinary 
ray. 

Extraordinary 
ray. 

Ordinary 
ray. 

Extraordinary 
ray. 

Quincke  (right-handed  quartz). 

Authority  :  Sarasin.* 

B 

I-53958 

1.54780 

c 

.  (J4O87 

r  JQ  "7  *i 

D 

•54335 

•55T99 

Cdi 

1.54227 

1.55124 

E 

.54649 

•555°8 

D 

Cd2 

.54419 
•54655 

•55335 

•55573 

F 
G 

.54868 
.55241 

.55758 
.56193 

Cd3 

•5^75 

•55595 

V-/Q4 

•54825 

•55749 

Cd5 
Cd6 

.55014 
•55104 

m 

Quincke  (left-handed  quartz). 

Cd7 

•55318 

.56270 

Cd9 

•56348 

•57319 

B 

1.54022 

1.54880 

Cdn 

Cd12 
Cd17 
Cd18 
Cd23 

.56617 
•56744 
•57094 
•58750 
.59624 
.61402 

•57599 
•57741 
.58097 
.59812 
.60713 
.62561 

C 
D 
E 
F 
G 

.54092 
.543i8 

•54575 
•54845 
.55246 

•54945 
•55245 
•55533 
.55801 
-56163 

Cd25 
Cd26 

.62502 
.63040 

.62992 
•63703 
.64268 

Auth'ority  :  Mascart. 

Zj\\%f 

•63569 

.64813 

Zn28 
Zn29 
A130 
Al3i 
A132 

.64041 
.64566 
.65070 
.65990 
.67500 

.65308 
.65852 
.66410 
.67410 
.68910 

A 
a 
B 
C 
D 
E 

1.53902 
54018 

•54099 
.54188 

.54423 
.54718 

1.54812 
•549r9 
•55002 
•55095 
•55338 
.55636 

b4 

•54770 

•55694 

F 

.54966 

•55897 

Authority:  Rubens. 

G 
H 

•55429 
•55816 

•56372 
.56770 

L 

M1 

.56019 

•56974 

•5615° 

.57121 

43-4(HY) 
48.5(F) 
59-o(G) 
65.6(0 

I-5538 
-5499 
.5442 
.5419 
•5376 

- 

N 
O 
P 

Q 

•R 

.  56400 
.56668 
.56842 

•57381 
.57659 
.57822 

.57998 
•58273 

OO.4 

•  ^64 

97-9 

•5353 

_ 

106.7 

•5342 

- 

Authority:  Van  der  Willigen  (left-handed  quartz). 

.   "7-4 

•5325 

- 

146.8 
167.9 

195-7 
234.8 

•5310 
.5287 
•5257 
.5216 
.5160 

- 

A 
B 
C 
D 

I-539H 
.54097 
•54185 

•54419 

1.54806 
.54998 
.55085 
.55329 

E 

.54715 

•55633 

c  cS  c  r 

G 

'    .55422 

•55°55 
•56365 

H 

.55811 

.56769 

SMITHSONIAN  TABLES. 


*  For  wave-lengths,  see  Tables  190  and  192. 

1 86 


INDEX    OF   REFRACTION. 

TABLE  194L  -  Uniaxial  Crystals. 


TABLES  194,  195. 


Substance. 

Line  of 
spec- 
trum. 

Index  of  refraction. 

Authority. 

Ordinary 
ray. 

Extraordi- 
nary ray. 

Alunite  (alum  stone)   

D 

red 
D 
D 
D 

y 

red 
red 

.  red  | 

green 
green 
D 

;' 

D 
red 
red 
red 
D 
D 
D 
D 
D 
D 

Dl 

red 
D 

1-573 
1-577 
2-5354 
1.6390 
1.6588 
1.589  to 
!-570 
1.560 
1.96 
2.854 
1.767  to 

1.769 
1.667 
1.584 
1.309 

1.719  to 

1.722 

r-539 
1.717 
1.564 

!-493 

1-459 
1-587 
1.446 
1.614 
1.997 
1.637 
i.  633  to 
1.650 
1.92 
1.924 

1.592 

4-524 

2-4959 
1.6345 
1.6784 
1.582  to 
1.566 
1.581 

3-199 
1-759 
1.762 
1.723 
1.578 

I-3I3 
1.717  to 
1.720 
I-54I 
i-5i5 
i-5i5 
1.501 
2.881 
1.467 
!-336 
2.452 

i-5i9 
2.093 
1.619 
i  .61  6  to 
1.625 
1.97 
1.968 

Levy  &  Lacroix. 
De  Senarmont. 
Schrauf. 

H 

DesCloiseaux. 
f  Various. 

Kohlrausch. 
De  Senarmont. 
DesCloiseaux. 

i    : 

Meyer. 
£  DesCloiseaux. 

Kohlrausch. 
Mallard. 
DesCloiseaux. 
De  Sernamont. 
Fizeau. 
Baker. 
Schrauf. 
Dufet 
Martin. 
Grubenman. 
Heusser. 

|  Jerofejew. 

De  Senarmont. 
Sanger. 

Ammonium  arseniate  

Benzil  

Beryl    ........ 

Calomel        

Corundum  (ruby,  sapphire,  etc.) 

Ice  at  —  8°  C  

Silver  (red  ore)    .        .      "  . 
Sodium  arseniate                                          , 
"       nitrate     .         .     .,  .        .        . 

Tin  stone      ....... 
Tourmaline  (colorless)        .... 

"           (different  colors)     .        .        • 
Zircon  (hyacinth)         .        .        . 

TABLE  195.— Biaxial  Crystals. 


Substance. 

Line  of 
spec- 
trum. 

Index  of  refraction. 

Authority. 

Minimum. 

Interme- 
diate. 

Maximum. 

Anglesite       .        . 
Anhydrite     . 
Antipyrin 
Aragonite 
Axinite 

D 

D 
D 
D 
red 

I.877I 

I-5693 
1.5101 

I-530I 
1.6720 

1.8823 

J-5752 

I.68I2 

1.6816 
1.6779 

1.8936 
1.6130 
1.6858 
1-6859 
I.68IO 

Arzruni. 
Mulheims. 
Glazebrook. 
Rudberg. 
DesCloiseaux. 

Barite   .... 

D 

1.636 

1-637 

1.648 

Various. 

Borax  .... 

D 

1.4467 

1.4694 

1.4724 

Dufet. 

Copper  sulphate  . 
Gypsum 

D 
D 

1.5140 
1.5208 

1.5368 
1.5228 

1-5433 
1.5298 

Kohlrausch. 
Mulheims. 

Mica  (muscovite)  . 
Olivine  .... 

D 
D 

1.5601 
I.66I 

1.5936 
1.678 

1-5977 
1.697 

Pulfrich. 
DesCloiseaux. 

Orthoclase    . 

D 

1.5190 

1.5237 

1.5260 

" 

Potassium  bichromate  . 
"          nitrate 
"          sulphate 
Sugar  (cane) 
Sulphur  (rhombic) 
Topaz  (Brazilian) 

Topaz  (different  kinds) 

D 
D 
D 
D 
D 
D 

Dl 

1.7202 
13346 
I  '4932 

1-5397 
I-9505 
1.6294 
1.630  to 
1.613 

1.7380 

1.5056 
1.4946 
1.5667 
2.0383 
1.6308 
1.631  to 
1.616 

1.8197 
1.5064 
1.4980 
1.5716 
2.2405 

I-6375 
1.637  to 
1.623 

Dufet. 
Schrauf. 
Topsoe  &  Christiansen. 
Catderon. 
Schrauf. 
Mulheims. 

>  Various. 

Zinc  sulphate 

D 

1.4568 

1.4801 

1.4836 

Topsoe  &  Christiansen. 

SMITHSONIAN  TABLES. 


187 


TABLE  1  96. 


INDEX   OF   REFRACTION. 

Indices  of  Refraction  relative  to  Air  lor  Solutions  of  Salts  and  Acids. 


Substance. 

Indices  of  refraction  for  spectrum  lines. 

Authority. 

Density. 

Temp.  C. 

D 

H, 

C 

P 

H 

(a)  SOLUTIONS  IN  WATER. 

Ammonium  chloride 

1.067 

27°-05 

1-37703 

I-37936 

I-38473 

1  -39336 

Willigen. 

1 

.025 

29-75 

•34850 

-3505° 

•355*5 

•36243 

* 

Calcium  chloride 

-398 

25-65 

.44000 

.44279 

•44938 

.46001 

4 

fl 

« 

it 

.215 

22.9 

•39411 

•39652 

.40206 

.41078 

1 

1 

« 

H 

•143 

25.8 

•37152 

•37369 

-37876 

.38666 

' 

' 

Hydrochloric  acid    . 
Nitric  acid  .... 

I.I66 

•359 

20-75 
18.75 

1.40817 

•39893 

1.41109 
.40181 

1.41774 
.40857 

1.42816 
.41961 

1 

« 

1  Potash  (caustic)  .     . 
Potassium  chloride  . 

.416       ii.o 
normal  solution 

.40052 
.34087 

.40281 
.34278 

.40808 
•34719 

I-35049 

•4*637 

Fraunhofer. 
Bender. 

" 

" 

double  normal 

.34982 

•35*79 

•35645 

•35 

7Q4 

- 

" 

" 

" 

triple  normal 

.35831 

.36029 

•365*2 

>9o 

- 

" 

Soda  (caustic)      .    . 
Sodium  chloride.  .     . 

1.376 

21.6 

18.07 

1.41071 
•37562 

I-4I334 

.37789 

1.41936 
.38322 

i.38~ 

746 

1.42872 

Willigen. 
Schutt. 

" 

.109 

18.07 

•35751 

-35959 

•36442 

-.36' 

1*3 

- 

" 

" 

" 

•035 

18.07 

.34000 

.34I91 

.34628 

.34969 

- 

" 

Sodium  nitrate     .    . 

1.358 

22.8 

1.38283 

1.385 

^ 

I-39I34 

_ 

1.40121 

Will  gen. 

Sulphuric  acid      .     . 

.811 

18.3 

•43444 

•436< 

>9 

.44168 

- 

.44883 

1 

u 

M 

•632 

I8.3 

.42227 

.42466 

•42< 

)07 

- 

•43 

^)4 

' 

u 

" 

.221 

I8.3 

•36793 

.37009 

-37468 

- 

•38 

158 

4 

" 

" 

.028 

18.3 

•33663 

.33862 

•34285 

- 

•3493s 

4 

Zinc  chloride   .    .    . 

J-359 

26.6 

1-39977 

1.40222 

1.40797 

_ 

1.41738 

« 

.    .    . 

.209 

26-4 

•37292 

.37515 

.38026 

- 

-38845 

(fc)  SOLUTIONS  IN  ETHYL 

ALCOHOL. 

Ethyl  alcohol  .     .    . 

0.789 

25-5 

i-3579i 

J-3597I 

I-36395 

- 

1.37094 

Willigen. 

" 

" 

•932 

27.6 

•35372 

.35556 

•35 

786 

.36662 

1 

' 

Fuchsin  (nearly  sat- 

urated)    . 

. 

_ 

16.0 

.3918 

•398 

.361 

•3759 

Kundt. 

Cyanin  (saturated)   . 

- 

16.0 

•3831 

•3705 

•3821 

NOTE.  —  Cyanin  in  chloroform  also  acts  anomalously;  for  example,  Sieben  gives  for 
a  4.5  per  cent,  solution  UA=  1.4593,  HB=  i-4695»  /*f(green)  =  1.4514,  M«  (blue)  =  1-4554- 
For  a  9.9  per  cent,  solution  he  gives  I*.A=  1.4902,  /t,p(green)  =  1.4497,  ^o(blue)  =  1.4597. 

(c)  SOLUTIONS  OF  POTASSIUM  PERMANGANATE  IN  WATER.* 

Wave- 
ength 

Spec- 
trum 

Index 
for 

Index 
for 

Index 
for 

Index 
for 

Wave- 
length 

Spec- 
trum 

Index 
for 

Index 
for 

Index 
for 

Index 
for 

X  io6. 

Hue. 

i  %  sol. 

2  %  SOI. 

3  %  sol. 

4  %  sol. 

X  10". 

line. 

I  %  SOI. 

2  %  SOl. 

3  %  sol. 

4  %  sol. 

68.7 

B 

1.3328 

1-3342 

_ 

L3382 

51.6 

_ 

1.3368 

I-3385 

_ 

_ 

65.6 

C 

•3335 

•3348 

'^S 

•339  ! 

5O.O 

- 

-3374 

.3383 

L3386 

1.3404 

6l.7 

— 

•3343 

•3365 

•3381 

.3410 

48.6 

F 

•3377 

.3408 

59-4 

- 

•3354 

•3373 

•3393 

.3426 

48.0 

- 

.338i 

•3395 

.3398 

•3413 

58-9 

D 

•3353 

.3372 

•3426 

46.4 

— 

•3397 

.3402 

•3414 

•3423 

56.8 

— 

•3362 

•3387 

-3412 

•3445 

44-7 

— 

-3407 

.3421 

.3426 

•3439 

55-3 
52-7 

E 

•3366 
•3363 

•3395 

•3417 

•3438 

43-4 
42-3 

— 

.3417 
•343* 

•3442 

•3457 

-3452 
.3468 

52.2 

" 

-3362 

•3377 

.3388 

" 

I 

SMITHSONIAN  TABLES. 


According  to  Christiansen. 

188 


TABLE  197. 


INDEX   OF   REFRACTION. 

Indices  of  Refraction  of  Liquids  relative  to  Air. 


Substance. 

Temp. 

Index  of  refraction  for  spectrum  lines. 

Authority. 

0 

D 

P 

Hr 

H 

Acetone     .... 

10° 

1.3626 

1.3646 

1.3694 

1-3732 

_ 

Korten. 

Almond  oil     ... 

O 

•4755 

.4782 

•4847 

_ 

Olds. 

Analin*     .... 

2O 

•5993 

•5863 

.6041 

.6204 

- 

Weegmann. 

Aniseed  oil     ... 

21.4 

.5410 

•5475 

•5647 

_ 

— 

Willigen. 

"          "... 

.5508 

•5572 

•5743 

- 

1.6084 

Baden  Powell. 

Benzene  t  •     -     •     • 

10 

1-4983 

1.5029 

1.5148 

- 

'•5355 

Gladstone. 

"            .... 

21-5 

•4934 

-4979 

•5°95 

— 

•53°4 

" 

Bitter  almond  oil    . 
Bromnaphtalin   .     . 

20 
20 

•5391 
•6495 

.6582 

•5623 
.6819 

•5775 
.7041 

.7289 

Landolt. 
Walter. 

Carbon  disulphide  J 

0 

1.6336 

i  -6433 

1.6688 

1.6920 

I-7I75 

Ketteler. 

u                     u 

20 

.6182 

.6276 

•6523 

.6748 

.6994 

u 

u                       u 

IO 

.6250 

•6344 

.6592 

.7078 

Gladstone. 

«<                   u 

T9 

.6189 

.6284 

•6352 

- 

.7010 

Dufet. 

Cassia  oil  .     .     .     . 

IO 

.6007 

.6104 

.6389 

— 

•7039 

Baden  Powell. 

"       "    . 

22.5 

•593° 

.6026 

.6314 

- 

.6985 

"   ' 

Chinolin     .... 
Chloroform    .     .     . 

20 

IO 

1.6094 
.4466 

1.6171 
•449° 

1.6361 
•4555 

1.6497 

.4661 

Gladstone. 
Gladstone  &  Dale. 

it 

3° 

•4397 

— 

.4561 

«                       u 

"             ... 

20 

•4437 

.4462 

•4525 

— 

— 

Lorenz. 

Cinnamon  oil      .     . 

23-5 

~J  *  •"" 

.6077 

.6188 

.6508 

- 

- 

Willigen. 

Ether                    .    . 

I  r 

I  3^4 

i  3;66 

1.3606 

_ 

1-3683 

Gladstone  &  Dale. 

1  j 
15 

o 

•3573 
•3677 

•3594 
•3695 

/- 
.3641 

•3739 

•3773 

•3713 

Kundt. 
Korten. 

Ethyl  alcohol      .     . 

U                       11 

IO 

•3636 

•3654 

.3698 

•3732 

— 

" 

"     '«     :  : 

20 

15 

.3596 
.3621 

.3614 
•3638 

.3657 
•3683 

.3690 

•3751 

M 

Gladstone  &  Dale. 

Glycerine  .... 
Methyl  alcohol  .     . 

20 
15 

1.4706 
•3308 

1.3326 

1.4784 
•3362 

1.4828 

.3421 

Landolt. 
Baden  Powell. 

Olive  oil    .... 

0 

.4738 

•4763 

•4825 

- 

- 

Olds. 

Rock  oil     .... 

o 

•4345 

•4573 

.4644 

~ 

mm 

Turpentine  oil    .     . 
Toluene     .... 

10.6 
20.7 
20 

.4692 
.4911 

1.4744 
.4721 
•4955 

1.4817 

•4793 
.5070 

,77o 

14939 

•49  i  3 

Fraunhofer. 
Willigen. 
Bruhl. 

Water  §     .     .  ~  — 
u 

16 
16 

•3336 
•3337 

•3377 
.3378 

•3409 

.3442 

Dufet. 
Walter. 

*  Weegmann  gives  fLD=  1.59668-. 000518 1.  Knops  gives  MP=  1-61500—  .00056*. 
t  Weegmann  gives  ,ur,=  1.51474  — -000665*.  Knops  gives  HD  =  1.51399  —  .000644*- 
%  Wiillner  gives  fic=  i. 63407  — -00078*;  HF=  1.66908  -.00082  t;  M/,  =  1.69215-  .00085*. 

§  Dufet  gives  »D=  .-33S97-  ^~7  <»5  *  + 20.6** —00043 5  <•—«>«  ,5/*)  between  o°  and  50°!  and  nearly  the 
same  variation  with  temperature  was  found  by  Ruhlmann,  namely,  Mo=  1-33373—  w—  (20. 14 *2  +  .000494 *<). 

SMITHSONIAN  TABLES. 

I89 


TABLE  198. 


INDEX   OF   REFRACTION. 


Indices  of  Refraction  of  Gases  and  Vapors. 

A  formula  was  given  by  Biot  and  Arago  expressing  the  dependence  of  the  index  of  refraction  of  a  gas  on  pressure  and 

temperature.      More  recent  experiments  confirm  their  conclusions.     The  formula  is  nt — i  —  — --, —    •      »  where 

i  -\-  aJ  760 

nt  is  the  index  of  refraction  for  temperature  t,  n0  for  temperature  zero,  a  the  coefficient  of  expansion  of  the  gas 
with  temperature,  and/  the  pressure  of  the  gas  in  millimetres  of  mercury.  Taking  the  mean  vaiue,  for  air  anrf 
white  light,  of  «0  —  i  as  0.0002936  and  a  as  0.00367  the  formula  becomes 

_      .OOO2c;36  /'  _     .0002891;        P 

i  -f-  .00367  t     1.0136  X  io6       i  +  .00367  io6' 
where  P  is  the  pressure  in  dynes  per  square  centimetre,  and  t  the  temperature  in  degrees  Centigrade. 


(a)  The  following  table  gives  some  of  the  values  obtained  for  the  different  Fraunhofer  lines  for  air. 

Index  of  refraction  according  to  — 

Spectrum 

Spectrum 

Index  of  refraction 
according  to 

line 

line. 
Ketteler. 

Lorenz. 

Kayser  &  Runge. 

Kayser  &  Runge. 

A                  1.0002929 

1.0002893 

1.0002905 

M 

1.0002993 

B                             2935 

2899 

2911 

N 

3003 

C                             2938 

2902 

2914 

U 

3015 

D                        2947 

2911 

2922 

E                        2958 

2922 

2933 

P 

1.0003023 

Q 

3°3I 

F                1.0002968 

1.0002931 

1.0002943 

R 

3°43 

G                        2987 

2949 

2962 

H                       3003 

2963 

2978 

S 

1.0003053 

K 

— 

2980 

T 

3064 

L 

— 

2987 

U 

3°75 

(b)  The  following  data  have  been  compiled  from  a  table  published  by  Brii  il  (Zeits.  fiir  Phys.  Chem.  vol.  7, 

pp.  25-27).     The  numbers  are  from  the  results  of  experiments  by  Biot  and  Arago,  Duloii{ 

;,  Jamin,  Ketteler, 

Lorenz,  Mascart,  Chappius,  Ray! 

eigh,  and  Riviere  and  Prytz.     When  the  number  given  re> 

ts  on  the  authority 

of  one  observer  the  name  of  that  observer  is  given.     The  values  are  for  o3  Centigrade  and  760  mm.  pressure. 

Substance. 

Kind  of 

light. 

Indices  of  refraction 
and  authority. 

Substance. 

Kind  of 
light. 

Indices  of  refraction 
and  authority. 

Acetone   .     .     . 
Ammonia      .     . 

D 

white 
D 

I.OOIO79-I.OOHOO 
1.000381-1.000385 
1.000373-1.000379 

Hydrogen     .     . 
Hydrogen  sul-  ( 

white 
white 
D 

1.000138-1.000143 
1.000139-1.000143 
1.000644  Dulong. 

Argon  .... 

D 

I. 

000281  Rayleieh. 

phide     .     .     / 

D 

1.000623  Mascart. 

Benzene    .     .     . 

D 

1.001700-1.001823 

Methane  .     .     . 

white 

1.000443  Dulong. 

Bromine   .     .     . 

D 

1.001152  Mascart. 

U 

D 

1.000444  Mascart. 

Carbon   dioxide 

white 
D 

i  .000449-1  .000450 
1.000448-1.000454 

Methyl  alcohol  . 
Methyl  ether     . 

D 
D 

1.000549-1.000623 
1.000891  Mascart. 

Carbon  disul-    j 
phide    .     .     / 

white 
D 

1.001500  Dulong. 
1.001478-1.001485 

Nitric  oxide  .     . 

«          a 

white 
D 

1.000303  Dulong. 
1.000297  Mascart. 

Carbon  mon-     } 

white 

1.000340  Dulong. 

Nitrogen  .     .     . 

white 

.000295-1.000300 

oxide     .     .     ) 

white 

1.000335  Mascart. 

"        ... 

D 

.000296-1  .000298 

Chlorine  .     .     . 

white 

1.000772  Dulong. 

Nitrous  oxide    . 

white 

.000503-1.000507 

"        ... 

D 

1.000773  Mascart. 

«           « 

D 

.000516  Mascart. 

Chloroform  .     . 

D 

1.001436-1.001464 

Oxygen     .     .     . 

white 

.000272-1.000280 

Cyanogen 

white 

1.000834  Dulong. 

... 

D 

1.000271-1.000272 

" 

D 

1.000784-1.000825 

Pentane    .     .     . 

D 

1.001711  Mascart. 

Ethyl  alcohol    . 

D 

1.000871-1.000885 

Sulphur  dioxide 

white 

1.000665  Dulong. 

Ethyl  ether  .     . 

D 

1.001521-1.001544 

"             " 

D 

1.000686  Ketteler. 

Helium    .     .     . 

D 

1.000043  Rayleigh. 

Water.     .     .     . 

white 

1.000261  Jamin. 

Hydrochloric    j 

white 

1.000449  Mascart. 

«     .     .     .     . 

D 

1.000249-1.000259 

acid  ...     | 

D 

1.000447 

SMITHSONIAN  TABLES. 


IQO 


ROTATION    OF   PLANE    OF    POLARIZED   LIGHT. 


TABLE   199. 


A  few  examples  are  here  given  showing  the  effect  of  wave-length  on  the  rotation  of  the  plane  of  polarization.  The 
rotations  are  for  a  thickness  of  one  decimetre  of  the  solution.  The  examples  are  quoted  from  Landolt  &  Born- 
stem  s  Phys.  Chem.  Tab."  The  following  symbols  are  used  :  — 

/  =  number  grammes  of  the  active  substance  in  100  grammes  of  the  solution. 
c  =  solvent  '• 

9  —  active         "  "    cubic  centimetre     " 

Right-handed  rotation  is  marked  +,  left-handed  — . 


Line  of 
spectrum. 

Wave-length 
according  to 
Angstrom  in 
cms.  X  io6. 

Tartaric  acid,*  CuH6O6, 
dissolved  in  water. 
9  =  50  to  95, 
temp.  =  24°  C. 

Camphor,*  C10H18O, 
diss«lved  in  alcohol. 
q  =  50  to  95, 
temp.  =  22.  g{J  C. 

Santonin.t  C15H,8O8, 
dissolved  in  chloroform. 
9  =  75  1096.5, 
temp.  =  20°  C. 

B 
C 
D 
E 

bi 
b2 
F 
e 

68.67 
65.62 

58>2; 

52.69 
5I-83 
5I-72 

48.61 

43-83 

+  2°.  748  +  0.09446? 
+  1.950+0.13030? 
+  0.153  +  0.17514? 

—  0.832  +  0.19147? 
—  3-598  +  0.23977  ? 
—  9.657  +  0.31437? 

38°-  549  —  0.0852? 
5I-945  —  0.0964? 
74-331—  0.1343? 

79.348  —  0.1451? 
99.601  —  0.1912? 
149.696  —  0.2346? 

—  140°.  I     +  0.2085  ? 
—  149.3    +0.1555? 
—  2O2-7    T  0.3086  ? 
—  285.6    +0.5820? 
—  302.38  +  0.6557  ? 

—  365-55  +  0.8284? 
534-98  +L5240? 

Santomn.t  C15H18O3,  * 
dissolved  in  alcohol. 
c=  1.782. 
temp.  =  20°  C. 

Santonin,t  Ci5H18O3, 

Santonicacid,t 

£&& 

dissolved  in 
chloroform. 
<T  =  27.ig2. 
temp.  =  20°  C. 

Cane  sugar,!: 
CuHKOu, 
dissolved  in 
water. 
P  =  io  to  30. 

dissolved  in 
alcohol. 
c  =  4.046. 
temp.  ~ 

20°  C. 

dissolved  in 
chloroform 
c=  3.  1-30.  5. 
temp.  = 

20°  C. 

B 
C 
D 
E 
bi 
b2 
F 
e 
G 
g 

68.67 
65.62 
58.92 
52.69 
5I-83 

5T-72 
48.61 

43-83 
43-°7 
42.26 

—  110.4° 
—  II8.8 

—  161.0 

—  222.6 

—  237.1 

—  261.7 
—  380.0 

442° 
504 
693 
991 

1053 
1323 

201  1 

23~8l 

484° 

549 
754 
1088 
1148 

1444 

22OI 
26lO 

-49° 
—  57 
—  74 
—  105 

—  112 

—  137 
—  I97 

—  230 

47°-56 
52.70 
60.41 
84.56 

87.88 
101.18 

131.96 

*  Arndtsen,  "  Ann.  Chim.  Phys."  (3)  54,  1858. 
t  Narini.  "  R.  Ace.  dei  Lincei,"  (3)13,  1882. 
*  Stefan,  "  Sitzb.  d.  Wien.  Akad."  52,  1865. 

ROTATION   OF    PLANE    OF    POLARIZED    LIGHT. 


TABLE  20O. 


Sodium  chlorate  (Guye,  C.  R.  108,  1889). 

Quartz  (Soret  &  Sarasin,  Arch,  de  Gen.  1882,  or  C.  R.  95,  1882).* 

Spec- 
trum 
line. 

Wave- 
length. 

Temp. 

Rotation 
per  mm. 

Spec- 
trum 
line. 

Wave- 
length. 

Rotation 
per  mm. 

Spec- 
trum 
line. 

Wave- 
length. 

Rotation 
per  mm. 

a 

71.769 

i5°-o 

2°.o68 

A 

76.04 

I2°.668 

Cd9 

36.090 

63°.  268 

B 

67.889 

17.4 

2.318 

a 

71.836 

14.304 

N 

35-818 

64-459 

C 
D 

65.073 
59.085 

20.6 

18.3 

2-599 
3.104 

B 

68.671 

I5-746 

Cdio 
O 

34.655 
34.406 

69-4S4 
70-587 

E 

W.2T.T, 

16.0 

3.841 

C 

65.621 

17.318 

F 

48.912 

11.9 

4-587 

D2 

58-95  I 

21.684 

Cdn 

34-015 

72.448 

G 

45-532 

IO.I 

5-331 

DI 

58-891 

21.727 

P 

33.600 

74-571 

G 
H 

42.834 
40.714 

14.5 

*3-3 

6.005 
6-754 

E 

52.691 

27.543 

Cd12 

32.858 
32.470 

78.579 
80.459 

L 
M 

38.412 

37-352 

14.0 
10.7 

7-654 
8.100 

F 
G 

48.607 
43.072 

32.773 
42.604 

R 

3I-798 

84.972 

N 
P 
Q 

35-544 
33-931 
32-341 

12.9 

I2.I 

8.861 
9.801 
10.787 

h 
H 

4I.OI2 
39.681 

47.481 

5I«I93 

Cdn 
Cd18 
Cd23 

27467 
25713 
23.125 

121.052 
143.266 
190.426 

R 
T 

30.645 
29.918 

J3-1 

12.8 

11.921 
12.424 

K 

39-333 

52-I55 

Cd24 

22.645 

201.824 

Cd17 
Cd18 

28.270 
25.038 

12.2 
II.6 

13.426 
14-965 

L 

M 

38.196 
27.262 

58.894 

Cd25 
Cd26 

2I-935 
21.431 

220.731 
235.972 

*  The  paper  is  quoted  from  a  paper  by  Ketteler  in  "  Wied.  Ann."  vol.  21,  p.  444-    The  wave-lengths  are  for 
the  Fraunhofer  lines,  Angstrom's  values  for  the  ultra  violet  sun,  and  Cornu's  values  for  the  cadmium  lines. 


SMITHSONIAN  TABLES. 


IQI 


TABLE  2O1 . 


LOWERING   OF   FREEZING-POINT   BY  SOLUTION   OF   SALTS. 


Under  P  is  the  number  of  grammes  of  the  substance  dissolved  in  100  cubic  centimetres  of  water.  Under  C  is  the 
amount  of  lowering  of  the  freezing-point.  The  data  have  been  obtained  by  interpolation  from  the  results  pub- 
lished by  the  authorities  quoted. 


Substance  and 
observer. 

P 

c° 

Substance  and 
observer. 

P 

c° 

Substance  and 
observer. 

P 

c° 

AgN03 
F.  M.  Raoult.* 

5 
10 

o-93 
1.71 

ZnS04 
F.  M.  Raoult.* 

i 

2 

0.10 

0.23 

MgCl2 
S.  Arrhenius.t 

I.O 

0.26 
o-53 

15 

2.38 

3 

0.36 

T-5 

0.81 

20 

2.97 

4 

0.49 

2.O 

1.  10 

25 

3-53 

5 

061 

2-5 

1.39 

3° 

4.00 

10 

1.23 

3-° 

1.69 

35 

4-43 

'5 

1.85 

3-5 

2.OO 

40 

4.80 

20 

2.50 

4.0 

2.32 

45 

5.15 

25 

3-T9 

4-5 

2.6| 

So 

5-45 

30 

3-94 

5-° 

2.98 

II 

5-75 
6.00 

CuS04 

I 

0.15 

1:1 

3-32 

3-67 

65 

6.26 

F.  M.  Raoult.* 

2 

0.29 

3 

0.40 

BaCl2 

0.5 

0.119 

Ca(NO3)2 

i 

0.28 

4 

0.51 

Harry  C.  Jones.§ 

I.O 

0.234 

F.  M.  Raoult.* 

2 

0.56 

5 

0.62 

1.5 

0-344 

3 

0.84 

6 

0.72 

2.O 

0.450 

4 

1.  12 

7 

0.82 

5 

1.40 

8 

0.92 

SrCl2 

0.5 

0.17 

10 

2.78 

9 

1.02 

S.  Arrhenius.  t 

I.O 

o-34 

15 

4.26 

10 

1.  12 

1-5 

0.50 

20 

6.00 

2.0 

0.65 

CdS04 

i 

0.09 

2-5 

0.80 

Cd(N03)2 

°-5 

O.II2 

F.  M.  Raoult* 

2 

0.19 

3-° 

o-95 

Harry  C.  Jones.§ 

I.O 

0.217 

3 

O.28 

3-5 

1.  12 

4 

0.38 

4.0 

1.29 

Na2SO4 

i 

0.28 

5 

0.48 

4-5 

1.44 

F.  M.  Raoult  * 

2 

3 

0.56 
0.84 

10 
15 

1.  00 

5-o 
5-5 

1.  60 
I.76 

4 

1.  12 

20 

2.11 

6.0 

i-93 

5 

1.40 

25 

2.77 

3° 

3-51 

CuCl2+2H2O 

°-5 

0.15 

K2SO4 

0.5 

O.I4 

35 

4.40 

S.  Arrhenius.t 

I.O 

0.30 

S.  Arrhenius. 

I.O 

0.27 

i-S 

0.44 

l-S 

o-39 

NaCl 

°-5 

0.32 

2.O 

0.58 

2.0 

0.51 

S.  Arrhenius.t 

I.O 

0.62 

2-5 

0.72 

2.5 

0.63 

1.5 

0.92 

0.86 

3-o 

o-74 

2.O 

1.22 

3-5 

.00 

3-5 
4.0 

0.85 
0.96 

2-5 

I.<J2 
1.82 

4.0 
4-5 

.14 
.29 

4-5 

1.07 

5-o 

•43 

5-5 

•17 

.27 

KC1 
Harry  C.  Jones.J 

I.O 

0.234 
0.464 

1:1 

•57 
•71 

6.0 

•37 

J-5 

0.693 

6.5 

1.85 

6.5 

•47 

2.0 

0.915 

2.O 

2.00 

7.0 

7-5 

1.67 

2-5 

3-° 

1.136 

J-359 

CdCl2 

o-5 

O.I  2O 

8.0 

1.77 

Harry  C.  Jones.§ 

I.O 

0.227 

LiCl 

°'5 

o-45 

1.5 

0.322 

MgS04 
F.  M.  Raoult* 

i 

2 

3 

0.18 

0-35 
0.52 

S.  Arrhenius.t 

I.O 
2.0 

0.89 

1-34 

1.78 

CaCl2 
S.  Arrhenius.t 

o-5 

I.O 
l.c 

0.23 
0-45 

0.68 

4 
5 

0.70 
0.89 

2-5 

2.23 

•*  J 
2.O 

0.91 

10 
15 

20 

i-77 
2.78 
3-68 

NH4C1 
Harry  C.  Jones.J 

I.O 

0.326 
0.644 
0-957 

2-5 

3-5 
4.0 

1.14 

i-37 
1.61 
1.85 

SMITHSONIAN  TABLES. 


*  In  "  Zeits.  fur  Physik.  Chem."  vol.  2,  p.  48g,  1888. 
t  Ibid.  vol.  2,  p.  491,  1888. 
$  Ibid.  vol.  u,  p.  no,  1893. 
§  Ibid.  vol.  n,  p.  529,  1893. 

192 


TABLE  201 


LOWERING   OF   FREEZING-POINT    BY   SOLUTION    OF   SALTS. 


Substance  and 
observer. 

P 

c° 

Substance  and 
observer. 

P 

C° 

Substance  and 
observer. 

P 

c° 

ZnCl2 

0-5 

0.185 

Alcohol,  C2H6O 

O.I 

0.044 

H2SO3 

o-5 

0.15 

Harry  C.  Jones.* 

I.O 

0.348 

Harry  C.  Jones.J 

O.2 

0.087 

S.  Arrhenius.t 

I.O 

0.30 

0.3 

0.129 

'•S 

0.45 

CdBr2 

°'5 

0.080 

0.4 

0.170 

2.O 

0.60 

Harry  C.  Jones.* 

I.O 

0.142 

0.212 

2.5 

o-75 

2.0 

0.195 
0.248 

I.O 

0.402 

3-0 

3-5 

0.90 
•05 

2-5 

0.300 

4.0 

.20 

3-° 

0.352 

4-5 

•35 

Acetic  acid, 

O.I 

0.034 

5-o 

•50 

CdI2 

j 

0.06 

C2H4O2 

O.2 

0.067 

5-5 

•65 

S.  Arrhenius.t 

2 

O.I  2 

Harry  C.  Jones.  J 

o-3 

0.099 

6.0 

.80 

3 

0.19 

0.4 

0.131 

6-5 

J.95 

4 

0.25 

o-5 

O.l62 

7-0 

2.IO 

5 

0.32 

I.O 

0.313 

10 

0.63 

H2SO4 

O.I 

0.044 

15 

0.92 

Harry  C.  Jones.J 

0.2 

0.088 

20 

1.22 

• 

0-3 

O.I3I 

25 

1.52 

P(OH)3 

0.5 

0.18 

0.4 

O.I72 

S.  Arrhenius.t 

I.O 

0-35 

o-5 

O.2I2 

NaOH 

O.I 

O.O92 

1.5 

0.50 

I.O 

O.4O2 

Harry  C.  Jones.  f 

O.2 

0.178 

2.O 

0.65 

O-3 

0.200 

H3P04 

o-5 

0.14 

0.4 

0-337 

S.  Arrhenius.t 

I.O 

0.27 

o-5 

0.410 

1.5 

0.38 

HI08 

0-5 

0.09 

2.O 

0.49 

KOH 

O.I 

0.064 

S.  Arrhenius.t 

I.O 

0.18 

2-5 

0.60 

Harry  C.  Jones.  J 

O.2 

0.126 

J-5 

0.27 

3-o 

0.70 

_    O-_ 

°-3 

0.189 

2.O 

o.35 

3.5 

O.oO 

0.4 

0.252 

2-5 

0.44 

A.O 

0.90 

o  c 

0.312 

3-o 

0.52 

0.6 
0.7 

0.370 
0.430 

3-5 
4.0 

4-5 

0.61 
0.69 
0.78 

Cane  sugar. 
F.  M.  Raoult.§ 

0-5 
I.O 

2.O 

0.030 
0.000 

0.118 

NH4OH 

0-05 

0.028 

5-° 

0.86 

3-0 

0.176 

Harry  C.  Jones.  J 

O.IO 

0.056 

4.0 

0.234 

0.15 

0.084 

5° 

0.292 

0.20 

0.113 

10.0 

0.587 

0.25 

0.143 

HC1 

O.I 

0.099 

15.0 

0.881 

Na2CO3 

O.I 

0.048 

Harry  C.Jones.| 

0.2 

0-3 

0.198 
0.296 

2O.O 
25.0 

1.174 
1.465 

Harry  C.  Jones.J 

O.2 

o-3 

0.096 
0.143 

0.4 

o-5 

0.395 
0-493 

30.0 

35-o 

1.752 
2.048 

0.4 

o.i  88 

40.0 

2.333 

o  ^ 

0.228 

w>  J 
I.O 

0.417 

HNO3 

O.I 

0.06  1 

Glycerine.il 
S.  Arrhenius.t 

I.O 

2.O 

O.22 
0.42 

K2CO3 
Harry  C.  Jones.  J 

O.I 
0.2 

°-3 

0.039 
0.078 
0.116 

Harry  C.  Jones.J 

0.2 

0-3 
0-4 

0.118 
0.175 
0.232 

3-o 

4.0 

C.Q 

2  _ 

0.64 
0.87 
I.  II 

0.4 
0.5 

0.152 
0.187 

0.1 

0.285 
0-33* 

o.o 
8.0 

I  '.83 

I.O 

0-343 

0.7 

0.390 

IO.O 
12.0 

2.32 
2-83 

*  In  "  Zeits.  fur  Physik.  Chem."  vol.  u,  p.  529.  l883- 
t  Ibid.  vol.  2,  p.  49i»  1888. 
$  Ibid.  vol.  12,  p.  623,  1893. 

I  5Fo%  ^u^\oiid^e"l\P4?C,  according  to  Fabian,  "Ding.  Poly.  Journ."vol.  ,55,  P-34S-    This  gives  an 
average  of  .3  per  gramme. 
SMITHSONIAN  TABLES. 

193 


TABLE  202. 

VAPOR    PRESSURE    OF  SOLUTIONS   OF   SALTS    IN   WATER 


The  first  column  gives  the  chemical  i™£  <**•£*  ' 

^  tenTperatureof  boiling  water  under  76  ce 


—  —  — 

—  —  — 

^—  —  —  — 

.—•——• 

I^MMM^MBM 

»—«•—•— 

Substance. 

0.5 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

8.0 

10.0 

A12(S04)8     . 
A1C13  . 

12.8 

22.5 

36-5 
61.0 

179.0 

318.0 

Ba(SO3)2     . 

6.6 

15.4 

34-4 

Ba(OH)2     .        . 

12.3 

22.5 

39-° 

Ba(NO3)2    -: 

13-5 

27.0 

Ba(ClO3)2   .-       » 

15.8 

33-3 

70-5 

108.2 

BaCl2  . 

16.4 

36-7 

77.6 

BaBr2  .... 
Ca(S03)2     . 
Ca(N08)2    .        « 

16.8 

9-9 
16.4 

38.8 
23.0 
34-8 

91.4 
56.0 
74.6 

150.0 
1  06.0 

139-3 

204.7 
161.7 

205.4 

Cad2.        •        • 
CaBr2. 

17.0 
17-7 

39-8 
44-2 

95-3 
105.8 

O    * 

166.6 

191.0 

241.5 
283-3 

368:5 

CdSO4 

4.1 

8.9 

18.1 

CdI2    .... 
CdBr2. 

7-6 
8.6 

14.8 
17.8 

33-5 
36-7 

52.7 

55-7 

80.0 

CdCl2.        .        •       '• 

9.6 

1  8.8 

36-7 

57-0 

77-3 

99-o 

Cd(N03)2   . 

15-9 

36.1 

78.0 

122.2 

Cd(C108)2  . 

17-5 

CoSO4 
CoCl2.        .        . 

5-5 
15.0 

10.7 
34-8 

22.9 
83.0 

45-5 
136.0 

186.4 

Co(NO8)2    .       V  '•'   • 

17-3 

39-2 

89.0 

152.0 

218.7 

282.0 

332.0 

FeSO432    .* 

5-8 

10.7 

24.0 

42-4 

H3B03 
H3P04 
H3AsO4       . 

6.0 
6.6 
7-3 

12.3 
14.0 

15.0 

30.2 

38-0 
45-2 
46.4 

51.0 
62.0 
64.9 

81.5 

103.0 

146.9 

189.5 

H2SO4 

12.9 

26.5 

62.8 

104.0 

148.0 

198.4 

247.0 

343-2 

KH2PO4     . 
KNO3. 

IO.2 
IO.3 

19-5 

21.  1 

33-3 
40.1 

47-8 

60.5 
74-5 

III 

85.2 

IO2.I 

126.3 

148.0 

KC1O3 

10.6 

21.6 

42.8 

62.1 

80.0 

KBrO3 

10.9 

22.4 

45-o 

KHSO4       . 

10.9 

21-9 

43-3 

65-3 

85-5 

107.8 

129.2 

170.0 

KN02 

ii.  i 

22.8 

44-8 

67.0 

90.0 

110.5 

130.7 

167.0 

198.8 

KC1O4 

"•5 

22-3 

KC1     .        .        . 

12.2 

24.4 

48.8 

74.1 

100.9 

128.5 

I|2.2 

KHCO2 

u.6 

23.6 

59-o 

77-6 

104.2 

132.0 

1  60.0 

210.0 

255.0 

KI                ... 

2C.-5 

52.2 

82.6 

1  1  2.2 

141.5 

I7I.8 

225.5 

278.5 

K2C2O4       .        . 

13.9 

28-3 

94-2 

I3I.O 

K2W04       .        . 

J3-9 

33-o 

75-o 

123.8 

1754 

226.4 

K2CO3 

14.4 

31.0 

68.3 

105-5 

I52.O 

209.0 

258.5 

350.0 

KOH  .... 

15.0 

29-5 

64.0 

99.2 

140.0 

181.8 

223.0 

309.5 

387.8 

K2Cr04       . 

16.2 

29-5 

60.0 

LiNO3 

12.2 

25-9 

55-7 

88.9 

122.2 

155.1 

1  88.0 

253-4 

309.2 

LiCl    .        . 
LiBr    .... 

I2.I 
12.2 

26.2 

57-i 
60.0 

95-o 
97-o 

J32-5 

I4O.O 

"75-5 
186.3 

219.5 
241.5 

341-5 

393-5 
438.0 

j  Li2SO4 

!3'3 

28.1 

56.8 

89.0 

LiHSO4      . 

12.8 

27.0 

57-o 

93-° 

I3O.O 

1  68.0 

Lil       . 

Li2SiFl6      . 

I3.6 
15-4 

28.6 
34-o 

64.7 
70.0 

105.2 
1  06.0 

I54-5 

206.0 

264.0 

357-0 

445-0 

LiOH  .... 
Li2CrO4       . 

1  6.4 

37-4 
32.6 

78.1 
74-o 

I2O.O 

171.0 

*  Compiled  from  a  table  by  Tammann,  "  Mem.  Ac.  St.  Petersb."  35,  No.  o,  1887.     See  also  Referate,  "Zeit.  f. 
Phys."  ch.  2,  42,  1886. 

SMITHSONIAN  TABLES. 

194 


TABLE  2O2, 
VAPOR    PRESSURE   OF   SOLUTIONS  OF   SALTS    IN   WATER. 


Substance. 

0.5 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

8.0 

10.0 

MgS04        .        .        . 

6'5 

I2.O 

24.5 

47-5 

MgCl2  

1  6.8 

39-o 

100.5 

183-3 

277.0 

377-0 

Mg(N03)2  . 

17.6 

42.0 

IOI.O 

174.8 

MgBr2 
MgH2(S04)2        . 

17.9 
18.3 

44-0 
46.0 

115.8 
116.0 

205-3 

298.5 

MnSO4 

6.0 

10.5 

2I.O 

MnCl2. 
NaH2PO4    . 
NaHSO4     . 

15.0 
10.5 
10.9 

34-o 

2O.O 
22.1 

76.0 

36.5 

47-3 

122.3 

75-o 

167.0 
66.8 

100.2 

209.0 
82.0 
126.1 

96.5 
148.5 

126.7 
'8>7 

157.1 
231.4 

NaNO3        .        .        . 

10.6 

22.5 

46.2 

68.1 

90-3 

111.5 

i3J.7 

167.8 

198.8 

NaC103       . 

10.5 

23.0 

48.4 

73-5 

98.5 

123-3 

147-5 

196.5 

223.5 

(NaPO3)6    • 

11.6 

NaOH 

1  1.8 

22.8 

48.2 

77-3 

107.5 

I39-I 

172-5 

243-3 

314.0 

NaNO2 

1  1.6 

24.4 

50.0 

75-o 

98.2 

I22.J 

146.5 

189.0 

226.2 

NaHPO4     . 

I2.I 

23.5 

43-o 

60.0 

78.7 

99-8 

I22.I 

NaHCO2     . 

I2.9 

24.1 

48.2 

77-6 

102.2 

127.8 

152.0 

198.0 

239.4 

NaSO4 

12.6 

25.0 

48.9 

74-2 

NaCl   .... 

12-3 

25.2 

52.1 

80.0 

I  II.O 

143.0 

176.5 

NaBrOg       . 
NaBr   .         ,        ... 

12.  1 

12.6 

25.0 
25.9 

54-1 

57-0 

81.3 
89.2 

108.8 
124.2 

136.0 
159.5 

I97-S 

268.0 

Nal               .         . 

I2.I 

"5-6 

60.2 

99-5 

136.7 

177-5 

22I.O 

301-5 

370.0 

Na4P2O7      . 

13.2 

22.O 

Na2C03 

14-3 

27-3 

53-5 

80.2 

III.O 

Na2C2O4      . 

14-5 

3O.O 

65-8 

105.8 

146.0 

Na2W04      .        : 

14.8 

33.6 

71.6 

115.7 

162.6 

Na3PO4       . 

16-5 

30.0 

52-5 

(NaP03)3    . 
NH4N03     . 

ll'.8 

36.5 
22.0 

42.1 

62.7 

82.9 

103.8 

I2I.O 

152.2 

180.0 

(NH4)2SiFl6 
NH4C1 

"•5 

I2.O 

25.0 
23-7 

44-5 
45-1 

69-3 

94-2 

118.5 

138.2 

179.0 

213.8 

NH4HSO4  . 
(NH4)2S04.        .        . 
NH4Br 
NH4I 

"•5 

II.O 

11.9 

12.9 

22.0 
24.0 

23.9 
25.1 

46.8 
46.5 
48.8 
49-8 

71.0 
69.5 
74.1 
78.5 

94-5 
93-o 
99-4 
104.5 

118. 
117.0 
121.5 
132-3 

139.0 

I4I.8 

156.0 

181.2 
190.2 

2OO.O 

2  1  8.0 

228.5 
243.5 

NiS04 

10.2 

21.5 

NiClo  .... 

16.1 

37-o 

86.7 

147.0 

212.8 

Ni(N03)2    . 

16.1 

37-3 

9r-3 

156.2 

235-0 

Pb(N03)2    .        .        . 

12^ 

23-5 

45-o 

63.0 

i  Sr(S03)2      . 

7-2 

20.3 

47.0 

Sr(N03)2     .        . 

15.8 

31.0 

64.0 

97-4 

i3T-4 

SrCl2  .         .        . 
SrBr2  .... 

1  6.8 
17.8 

38.8 
-42.0 

91.4 

IOI.I 

156.8 
179.0 

223-3 
267.0 

281.5 

ZnS04          .        ...        • 
ZnCl2  -         .        •      •  • 
Zn(N03)2     .        .        . 

4-9 
9.2 
16.6 

10.4 
18.7 
39-o 

21.5 
46.2 
93-5 

42.1 

157.5 

107.0 
223.8 

.53.° 

I95.0 

11, 

: 

SMITHSONIAN  TABLES. 


'195 


TABLE  2O3. 

RISE   OF   BOILING-POINT  PRODUCED  BY  SALTS  DISSOLVED  IN  WATER.* 

This  table  gives  the  number  of  grammes  of  the  salt  which,  when  dissolved  in  100  grammes  of  water,  will  raise  the 
boiling-point  by  the  amount  stated  in  the  headings  of  the  different  columns.  The  pressure  is  supposed  to  be  76 
centimetres. 


Salt. 

IOC. 

2° 

3° 

4° 

5° 

7° 

10° 

15° 

20° 

25° 

BaCl2  -f  2H2O    . 
CaCl2 
Ca(NO3)2  -f  2H2O     . 

15.0 
6.0 

I2.O 

"•5 

25-5 

47-3 
16.5 

39-5 

63.5 
21.0 

53-5 

(7J.6g 

sg 

ves  4° 
32.0 
98.7 

.5  rise 

152-5 

of  temp 

55-5 
240.0 

69.0 
331-5 

84-5 
443-5 

KOH 

4-7 

9-3 

13.6 

17.4 

20.5 

26.4 

34-5 

47-o 

57-5 

67-3 

KC2H3O2   .        .        . 

6.0 

I2.O 

1  8.0 

24-5 

31.0 

44.0 

63.5 

98.0 

134.0 

171-5 

KC1     . 

9.2 

I6.7 

23-4 

29.9 

36-2 

484 

(57-4 

;ives  a  rise  of  8°.  5) 

K2CO8 

"•5 

22-5 

32.0 

40.0 

47-5 

60.5 

78.5 

103.5 

127-5 

152-5 

1  KC1O8 

13.2 

27.8 

44-6 

62.2 

KI       .        .        . 

15.0 

3O.O 

60.0 

74-o 

99-5 

134- 

185.0 

(220  gives  i8°.5) 

KNO3 

15.2 

3I.O 

47-5 

64-5 

82.0 

120.5 

188.5 

338.5 

K2C4H4O6  -f  £H2O 

18.0 

36.0 

54-o 

72.0 

90.0 

126.5 

182.0 

284.0 

KNaC4H4O6       . 

I7'3 

34-5 

51-3 

68.1 

84.8 

119.0 

171.0 

272.5 

390.0 

510.0 

KNaC4H406  +  4H20 

25.0 

53-5 

84.0 

1  1  8.0 

I57.o 

266.0 

554-o 

55IO-o 

LiCl    .... 
LiCl+2H2O      . 

3-5 
6-5 

7.0 
13.0 

IO.O 

19.5 

12.5 
26.0 

15.0 
32.0 

18.5 
44.0 

26.0 
62.0 

35-o 
92.0 

42-5 
123.0 

50.0 
160.5 

MgCl2  +  6H2O  . 

1  1.0 

22.0 

33-0 

44.0 

55-0 

77-o 

I  IO.O 

170.0 

241.0 

334-5 

MgS04  +  7H2O 

41.5 

87.5 

138.0 

196.0 

262.0 

NaOH 

4-3 

8.0 

"•3 

14-3 

17.0 

22.4 

30.0 

41.0 

51.0 

60.  i 

NaCl  .... 

6.6 

12.4 

17.2 

21.5 

25-5 

33-5 

(40.7  gives  8°.8  rise) 

NaNO3 

9.0 

18.5 

28.0 

38.0 

48.0 

68.0 

99-5 

156.0 

222.O 

NaC2H3O2  +  3H2O  . 

14.9 

30.0 

46.1 

62.5 

79-7 

118.1 

194.0 

484.0 

6250.0 

Na2S2O3      . 

14.0 

27.0 

39-o 

49-5 

76.0 

104.0 

147.0 

214.5 

302.0 

Na2HP04  . 

17.2 

34-4 

514 

68.4 

85.3 

Na2C4H406  +  2H2O  . 

21.4 

44-4 

68.2 

93-9 

121.3 

183.0 

(237-3  g'ves  8°4  rise) 

Na2S203  +  5H20       . 

23.8 

50.0 

78.6 

108.1 

139-3 

216.0 

400.0 

1765.0 

Na2CO3  +  ioH2O      . 

34-1 

86.7 

177.6 

369-4 

1052.9 

Na2B4O7  +  ioH2O     . 

39- 

93-2 

254-2 

898.5 

(5555-5  gives  4°.$  rise 

NH4C1 

6.5 

12.8 

19.0 

24.7 

29.7 

39-6 

56.2 

88.  c 

NH4NO3     . 

IO.O 

2O.O 

30.0 

41.0 

52.0 

74-o 

108.0 

172.6 

248.0 

337-0 

NH4S04     . 

15-4 

3O.I 

44-2 

58.0 

71.8 

99.1 

(115.3  gives  108.2) 

SrCl2  +  6H2O    . 

2O.O 

4O.O 

60.0 

81.0 

103.0 

150.0 

234.0 

524.0 

Sr(N03)2     . 

24.0 

45-o 

63.6 

81.4 

97.6 

C4H606       .        .        . 

17.0 

34-4 

52.0 

70.0 

87,0 

123.0 

177.0 

273.0 

374-0 

484.0 

C2H204  +  2H2O 
C6H807  -f  H2O 

I9.O 
29.0 

40.0 
58.0 

62.0 
87.0 

86.0 
1  1  6.0 

II2.O 
145.0 

169.0 
208.0 

262.0 
320.0 

536.o 
553-o 

1316.0 
952.0 

50000.0 

Salt.                    40°        60° 

80° 

100° 

120° 

140° 

160° 

180°       200°      240° 

CaCl2  .        .        .     137.5     222.0 

314.0 

KOH   .        .        .      92.5      121.7 
NaOH       '  .        .      93.5     150.8 
NH4NO3      .        .    682.0    1370.0 

152.6 
230.0 
2400.0 

185.0 

345-c 
4099-c 

219.8 

526.3 
8c;47.c 

263.1 
8oo.c 

00 

312.5 
1333-0 

375.0      444.4    623.0 
2353-0    6452.0        - 

C4H6()6        .        .    980.0   3774.0 

(infinity  gives  170) 

*  Compiled  from  a  paper  by  Gerlach,  "  Zeit.  f.  Anal.  Chem."  vol.  26. 
SMITHSONIAN  TABLES. 

196 


TABLE  204. 


CONDUCTIVITY   FOR    HEAT. 

Metals  and  Alloys. 

The  coefficient  k  is  the  quantity  of  heat  in  therms  which  is  transmitted  per  second  through  a  plate  one  centimetre 
thick  per  square  centimetre  of  its  surface  when  the  difference  of  temperature  between  the  two  faces  of  the  plate- 
is  one  degree  Centigrade.  The  coefficient  k  is  found  to  vary  with  the  absolute  temperature  of  the  plate,  and  is  ex~ 
pressed  approximately  by  the  equation  kt  —  &0  (i  -f-  »*)•  In  the  table  k0  is  the  value  of  kt  for  o°  C,  t  the  tempera- 
ture Centigrade,  and  a  a  constant. 


Substance. 

t 

» 

a 

} 

Substance. 

t 

" 

i 

* 

3 

Aluminium    .     .  j 

0 
IOO 

0-3435  I 
•36l9  f 

.0005356 

I 

Clay  slate, 
(Devonshire)  . 

.00272 

6 

Antimony  .     .     .  < 

o 

IOO 

.0442  ) 
.0396  \ 

—  .001041 

I 

Granite.    .    .  {  *% 

_ 

.00510 

.00550 

I6 

Bismuth    .     .    .  j 

o 

IOO 

.0177 
.0164 

—  -000735 

I 

Slate  : 
along   cleav-    from 

_ 

.00550 

1* 

Brass  (yellow)    .  j 

0 
IOO 

.2041 
.2540 

.002445 

I 

age  ...       to 
across  cleav-    from 

: 

.00650 

.00315 

1 
6 

'«      (red)     .     .] 

o 

IOO 

.2460  i 
.2827  \ 

.001492 

I 

age  .    .    .      to 

Marbles,      in- 

"• 

.00360 

1° 

Cadmium  .     .     .  j 

o 

.2200  / 
.2045  f 

—  .000705 

I 

cluding  lime- 
stone,      cal-    from 

_ 

.00470 

u 

^A/J/T/TAXf 

*"    0 

1.0405 

.000039 

2 

cite,     and       to 

- 

.00560 

r 

<s>roper^^__---~-r^ 

0 

-.7189 

compact  do- 

IOO 

.7226 

.000051 

I 

lomite      .    . 

German  silver    .  < 

0 
IOO 

.0700 
.0887 

.002670 

I 

Micaceous  flagstone  : 
along  cleavage    .     . 

_ 

.00632 

6 

Iron       .     .     .     .  < 

o 

IOO 

.1665  ( 

.1627  i 

—  .000228 

I 

across  cleavage  .     . 
Sand  (white  dry)  .     . 

_ 

.00441 

.00093 

6 
6 

"     (wrought)  *  | 
Lead     .    .     .     .  j 

o 

IOO 

o 

IOO 

o 

.2070  j 

•1567  t 
.0836  » 
.0764  \ 
.0148  1 

—  .000861 

3 

i 

Sandstone  and  (  f 
hard  grit    frt°om 
(dry)    .    .    .(    ' 
Serpentine 
(Cornwall  red)   .    . 

- 

.00545 
.00565 

.00441 

H 

6 

Mercury    .     .     .  < 

50 

O-IOO 

.0189  f 
.0201 

.001267 

4 

2 

Snow      in     compact 

Magnesium    .     . 
Steel  (hard)   .     . 
"      (soft)    .     . 
Silver    .... 

O-IOO 

o 

.3760 
.0620 

.1110 

1.0960 

.000000 

I 

5 
5 
4 

Icivcrs                       • 

- 

.00051 
.0013 

.00045 
.00033 

6 
8 
8 

Plaster  of  Paris     .    . 
Pasteboard  .... 
Strawboard  .... 

Tin  •! 

o 

IOO 
0 

.1528 

.1423  J 
•0319  t 
.3030  f 

—  .000687 

4 

2 

Paraffin   .     .    .    .    < 
Sawdust  

0 
IOO 

.00014 

.00023 
.00168 

.00012 
.00087 

9 
10 

Wood's  alloy 

Zinc  

Vulcanite     .... 

Vulcanized]  from 

_ 

.00034 

6 

rubber  (soft)  (    to 

- 

.00054 

6 

Wood,  Fir  : 

parallel  to  axis   .     . 

- 

.OOO3 

8 

perpendicular       to 

axis    

"™ 

.OOOO9 

Wax  (bees)  .... 

" 

.00009 

8 

AUTHORITIES. 

?  T   Forbes                   5  Kohlrausch.          7  Hjeltstrom.        '   9  £•  Weber. 
2  Berg"et           \  HF   Weber.           6  H.  L.  &  D.t           8  G.  Forbes.           10  Stefan. 

*  A  repetition  of  Forbes's  experiments  by  Mitchell,  under  the  direction  of  Tait,  shows  the  conductivity  to  increase 

with  rise  of  temperature.     (Trans.  R.  S.  E.  vol.  33,  '88?.) 
t  Herschel,  Lebour,  and  Dunn  (British  Association  Commit) 

SMITHSONIAN  TABLES. 

197 


TABLES  205-208, 


CONDUCTIVITY    FOR    HEAT. 


TABLE  205.— Various  Substances. 


TABLE  206. —Water  and  Salt  Solutions. 


Substance. 

* 

kt 

Au- 
thor- 
ity. 

o 

0 

o 

0 

49 
o 

0 

.000405 
.000162 

.000717 
.000043 
.000033 

.002000 
.OOO37O 
.OOOO87 
.000035 
.0005       ) 
.0023       J 
.OOOO87 
.000042 
.00223 
.00568 

•00433 
.00211 

I 

I 
I 
I 

2 
2 

3 
i 
i 

i 
4 

2 
2 

Cement      .... 
Cork      
Cotton  wool  .     .     . 
Cotton  pressed  .     . 
Chalk    
Ebonite      .... 
Felt 

Flannel      .... 

G'H<oom:  :  : 

Haircloth  .... 
Ice                   ,     . 

ice    ...          .    -j 

Caen  stone  (build-  ) 
ing  limestone)  .  f 
Calcareous  sand-     \ 
stone  (freestone)  f 

AUTHORITIES. 

i  G.  Forbes.             3  Various. 
2  H.,  L.,  &  D*        4  Neumann. 

Au- 

Substance. 

Density. 

* 

fcf 

thor- 

ity. 

Water      .    /' 

_ 

_ 

.002 

, 

14 

— 

o 

.00120 

2 

"                   .        . 

- 

9-15 

.00136 

2 

tt 

— 

4 

.OOI29 

3 

« 

— 

3° 

.00157 

4 

" 

— 

18 

.00124 

5 

Solutions  in 

water. 

CuS04     .     . 

.160 

4.4 

.OOIlS 

2 

KC1     .     .     . 

.026 

:3 

.00116 

4 

NaCl  .     .     . 

33*% 

10-18 

.00267 

6 

H2SO4     .     . 

•054 

20.5 

.OOI26 

5 

« 

.100 

20.5 

.00128 

5 

« 

.180 

21 

.00130 

5 

ZnSO4     .     . 

•134 

4-5 

.OOIlS 

2 

« 

.136 

4-5 

.00115 

2 

AUTHORITIES. 

i  Bottomlev.                4  Graetz. 

2  H.  F.  Weber.           5  Chree. 

3  Wachsmuth.             6  Winkelmann. 

TABLE  207.  —  Organic  Liquids. 


TABLE  208. -Gases. 


Substance. 

* 

Jet 

Xiooo 

f 

a 

>, 

1 
< 

2 

3 
3 

2 
2 

Acetic  acid  .     .     . 
Alcohols  :  amyl    . 
ethyl   . 
methyl 
Carbon  disulphide 
Chloroform  .     .     . 
Ether 

9-15 
9-15 
9-15 
9-15 
9-15 
9-15 
9-1  5 
9-i5 

T3 
J3 

.472 
.328 
423 

•495 

•m 
n 

•395 
•425 
•355 
•325 

O.I2 

.Oil 
.0067 

Glycerine     .     .     . 
Oils  :  olive  .     .     . 
castor     .     . 
petroleum  . 
turpentine  . 

AUTHORITIES. 
i  H.  F.  Weber.   2  Graetz.    3  Wachsmuth. 

Substance. 

* 

Xiooo 

a 

a 

3 

«5 

Air 

o 

.<68 

OOIQO 

Ammonia    .     .     . 
Carbon  monoxide 

o 

0 

.458 
•499 

.00548 

"      dioxide    . 

o 

•3°7 

- 

Ethylene      .     .     . 
Hydrogen    .     .     . 
Methane  .... 

0 

o 

7-8 

•395 
.647 

.00445 
.00175 

Nitrogen      .     .     . 
Nitrous  oxide  .     . 

7-8 
7-8 

•524 
•35° 

.00446 

Oxygen   .... 

7-8 

•563 

AUTHORITY. 

i  Winkelmann. 

*  Herschel,  Lebour,  and  Dunn  (British  Association  Committee). 


SMITHSONIAN  TABLES. 


TABLE  2O9. 


FREEZING    MIXTURES.' 


Column  i  gives  the  name  of  the  principal  refrigerating  substance,  A  the  proportion  of  that  substance,  B  the  propor- 
tion of  a  second  substance  named  in  the  column,  C  the  proportion  of  a  third  substance,  D  the  temperature  of 
the  substances  before  mixture,  E  the  temperature  of  the  mixture,  F  the  lowering  of  temperature,  G  the  tempera- 
ture when  all  snow  is  melted,  when  snow  is  used,  and  H  the  amount  of  heat  absorbed  in  heat  units  (therms  when 
A  is  grammes).  Temperatures  are  in  Centigrade  degrees. 


Substance. 

A 

B 

C 

D 

E 

F 

G 

H 

NaC2H3O2  (cryst.) 
NH4C1  . 

30 

H2O-ioo 

- 

10.7 

—  4-7 
—  5-1 

I5-4 
l8.4 

- 

- 

NaNO3  . 

75 

"       " 

— 

13.2 

I8.5 

_ 

— 

Na2S2O3  (cryst.)    . 

no 

«       « 

- 

10.7 

—  8.0 

I8.7 

- 

- 

KI. 

140 

«       a 

- 

10.8 

—  11.7 

22.5 

- 

— 

CaCl2  (cryst.) 

250 

U                  U 

- 

10.8 

—  12.4 

23.2 

- 

- 

NH4NO3       . 

60 

«                 U 

— 

13.6 

—  13.6 

27.2 

- 

— 

(NH4)2S04   .        . 

25 

"              50 

NH4N03-25 

26.O 

- 

- 

NH4C1  . 

25 

it                U 

"          " 

- 

— 

22.0 

— 

— 

CaCl2    . 

25 

((                  41 

"          " 

— 

— 

20.0 

— 

— 

KN03    . 

25 

«               U 

NH4Cl-25 

- 

- 

20.0 

- 

- 

Na2SO4 

25 

"       " 

"        " 

- 

- 

19.0 

- 

- 

NaN03. 

25 

«               U 

«        .< 

— 

- 

17.0 

— 

— 

K2SO4  . 

10 

Snow  100 

- 

— 

—  1.9 

0-9 

- 

Na2CO3  (cryst.)     . 
KN03    . 

20 
13 

U                 44 

_ 

— 

—  2.O 
-2.8S 

I.O 
1.85 

: 

_ 

CaCl2     . 

30 

«                 « 

— 

— 

—  10-9 

9-9 

— 

— 

NH4C1  . 

25 

44          11 

— 

— 

—  15-4 

14.4 

- 

— 

NH4NO3 

45 

«                 H 

— 

— 

—  16.75 

15-75 

— 

— 

NaN03. 

5° 

1                 « 

- 

— 

—  17-75 

16.75 

— 

- 

NaCl      . 

33 

<         it 

— 

— 

—  21-3 

20.3 

— 

— 

'    1.097 

— 

— 

—  37-0 

36.0 

—37.0 

O.O 

'    1.26 

_ 

— 

—  36.0 

35-o 

—30.2 

17.0 

H2SO4+H2O 
(66.i%H2S04) 

1  1.38 

'    2.52 
'   4.32 

- 

— 

—  35-0 
—  30.0 
—  25.0 

34-o 
29.0 
24.0 

—25.0 
—12.4 

—  7-0 

27.0 
133-0 
273.0 

'    7-92 

— 

— 

—  2O.O 

19.0 

—  3-1 

553-0 

'  13-08 

_ 

— 

—  16.0 

15.0 

—  2.1 

967.0 

"  0.35 

— 

o 

— 

— 

0.0 

52.1 

"       -49 

- 

o 

- 

- 

—  19.7 

49-5 

"     .61 

_ 

o 

— 

- 

—  39-0 

40-3 

CaCl2  +  6H20      - 

«     .70 
«     .81 

- 

0 

o 

: 

— 

—  54-9t 
—  40-3 

30.0 
46.8 

"    1.23 

- 

o 

- 

- 

—  21.5 

S8.5 

"    2.46 

— 

o 

— 

- 

—  9.0 

192.3 

"     4-92 

- 

0 

- 

- 

—  4.0 

392.3 

Alcohol  at  4°        j 

77 

CO2  solid 

: 

0 

—30.0 
—72.0 

_ 

_ 

- 

Chloroform    . 

- 

U               U 

- 

- 

—77.0 

— 

— 

— 

Ether     . 

_ 

tt       « 

— 

— 

—77.0 

— 

™* 

Liquid  SO2    . 

- 

H20-.75 

~- 

20 

—82.0 

- 

- 

33-0 

•94 

- 

20 

—4.0 

— 

— 

2I.O 

_ 

10 

—4.0 

— 

— 

34-o 

«       « 

_ 

5 

—4.0 

- 

- 

40.5 

Snow     " 

_ 

o 

—4.0 

— 

- 

122.2 

NH4NO3       . 

H2O-i.20 

Snow     " 

— 

IO 

o 

—  14.0 
—  14.0 

- 

- 

17.9 
129.5 

H2O-i.3i 

— 

10 

-I7-5J 

- 

- 

10.6 

Snow     " 

— 

o 

—  17.5* 

— 

— 

I3I-9 

H2O-3-6i 

- 

10 

—  8.0 

o   _ 

— 

- 

0.4 

Snow     " 

o 

—  o.o 

Compiled  from  the  results  of  Caffletet  and  Colardeau,  Hammerl,  Hanamann,  Moritz,  Pfanndler,  Rudorf,  and 
Tollinger. 

t  Lowest  temperature  obtained. 


SMITHSONIAN  TABLES. 


199 


TABLE  210. 

CRITICAL    TEMPERATURES,    PRESSURES,    VOLUMES,    AND     DENSITIES 

OF    CASES.* 

6  =  Critical  temperature. 
P=  Pressure  in  atmospheres. 

^>  =  Volume  referred  to  air  at  o°  and  76  centimetres  pressure. 
</=  Density  in  grammes  per  cubic  centimetre. 


Substance. 

e 

P 

4> 

d 

Observer. 

Air          

—  140.0 

39-o 

Olszewski. 

Alcohol  (C2H6O)   . 
"... 

243.6 
233-7 

62.76 

0.007  1  3 

0.288 

Ramsay  and  Young. 
Jouk  (lowest  value 

recorded). 

"      (CH40)     .        .        .- 

239-95 

78.5 

- 

- 

Ramsay  and  Young. 

Ammonia        .... 

130.0 

115.0 

_ 

_ 

Dewar. 

Argon     

—  I2I.O 

50.6 

_ 

1-5 

Olszewski. 

288.  s 

47.0 

0.00981 

O.^S 

Young. 

Carbon  dioxide 

"-"-"o 
30.92 

TV     s 

77 

0.0066 

*JJJ 

Andrews. 

"       monoxide  . 

—  141.1 

35-9 

— 

— 

Wroblewski. 

"       disulphide  . 

277.7 

78.1 

_ 

_ 

Dewar. 

Chloroform     .... 

260.0 

54-9 

- 

- 

Sajotschewski. 

Chlorine         .... 

141.0 

83-9 

_ 

_ 

Dewar. 

"                .... 

148.0 

- 

- 

Ladenburg. 

Ether      

19.7 

35-77 

0.01584 

0.208 

Battelli. 

"          

194.4 

35-6i 

0.01344 

0.246 

Ramsay  and  Young. 

Ethylene          .... 

9.2 

58.0 

— 

— 

Van  der  Waals. 

« 

13.0 

- 

0.00569 

0.21 

Cailletet. 

Hydrogen        .... 

—  22O.O 

2O.O 

_ 

_ 

Olszewski. 

"         chloride 

5I-25 

86.0 

_ 

_ 

Ansdell. 

it               n 

52-3 

86.0 

_ 

0.61 

Dewar. 

"         sulphide 

IOO.O 

88.7 

- 

- 

Olszewski. 

Methane          .... 

—81.8 

54-9 

— 

_ 

" 

M 

—99-5 

50.0 

- 

- 

Dewar. 

Nitric  oxide  (NO)  . 
Nitrogen          .... 

—93-5 
—  146.0 

71.2 
35-o 

- 

0-44 

Olszewski. 

it 

—  146.0 

33-o 

— 

Wroblewski. 

"        monoxide  (N2O) 

354-0 

75-o 

- 

- 

Dewar. 

Oxygen    

—118.0 

50.0 

_ 

0.6044 

Wroblewski. 

Sulphur  dioxide 

*5M 

78.9 

- 

- 

Sajotschewski. 

"            "          .     '    . 

157-0 

— 

— 

— 

Clark. 

Water     

1^8.1 

_ 

0.001874 

0.4.20 

Nadejdine. 

jjw  •* 
370.0 

195-5 

**»T*!5P 

Dewar. 

*  Abridged  for  the  most  part  from  Landolt  and  Boernstein's  "  Phys.  Chem.  Tab." 

NOTE.  —  Guldberg  shows  (Zeit.  fur  Phys.  Chem.  vol.  5,  p.  375)  that  for  a  large  number  of  organic  substances  the 
ratio  of  the  absolute  boiling  to  the  absolute  critical  temperature,  although  not  constant,  lies  between  0.58  and  0.7,  the 
majority  being  between  .65  and  .7.     Methane,  ethane,  and  ammonia  gave  approximately  0.58.     HaS  gave  .566,  and 
CS2,  N2O,  and  O  gave  about  .59. 
SMITHSONIAN  TABLES. 


200 


TABLE  21 1 


HEAT   OF   COMBUSTION. 

Heat  of  combustion  of  some  common  organic  compounds. 
Products  of  combustion,  CO2  or  SO2  and  water,  which  is  assumed  to  be  in  a  state  of  vapor. 


Substance. 

Therms  per 
gramme  of 
substance. 

Authority. 

Acetylene    

11923 

Thomsen. 

Alcohols  :  Amyl 

8958 

Favre  and  Silbermann. 

Ethyl 

7183 

«. 

Methyl       . 

53°7 

«       «              " 

0077 

Stohmann,  Kleber,  and  Langbein. 

Coals  :  Bituminous     . 

-7~/  / 

7400-8500 

Various. 

Anthracite     . 

7800 

Average  of  various. 

Lignite   .... 

6900 

«         «       « 

Coke      .... 

7000 

"         "       " 

Carbon  disulphide 

3244 

Berthelot. 

Dynamite,  75%  . 

1290 

Roux  and  Sarran. 

Gas  :  Coal  gas    .... 

5800-11000 

Mahler. 

Illuminating      . 

5200-5500 

Various. 

Methane    .... 

13063 

Favre  and  Silbermann. 

Naphthalene     . 

9618-9793 

Various. 

Gunpowder         .... 

720-750 

" 

Oils:  Lard          .        ,f-     . 

9200-9400 

" 

Olive         . 

9328-9442 

Stohmann. 

Petroleum,  Am.  crude 

11094 

Mahler. 

"             "     refined    . 

11045 

" 

"           Russian  . 

10800 

" 

Woods  :  Beech  with  12.9%  H2O 

4168 

Gottlieb. 

Birch    «     11.83      " 

4207 

" 

Oak      "     13-3 

399° 

" 

Pine      "     12.17      " 

4422 

" 

SMITHSONIAN  TABLES. 


201 


TABLE  212, 


Heat  of  combination  of  elements  and  compounds  expressed  in 


HEAT   OF 


Substance. 

Combined 
with  oxygen 
forms  — 

Heat 
units. 

Combined 
with  chlorine 
forms  — 

Heat 
units. 

Combined 
with  sulphur 
forms  — 

Heat 

units. 

|. 

3  £? 
<- 

Calcium    . 

CaO 

3284 

CaCl2 

4255 

CaS 

2300 

I 

Carbon  —  Diamond  . 

C02 

7859 

- 

- 

— 

— 

2 

«                   "."""•"« 

CO 

2141 

— 

— 

— 

~ 

3 

"      —  Graphite  . 

C02 

7796 

- 

- 

- 

— 

3 

Chlorine    .... 

C12O 

—  254 

— 

— 

~ 

~ 

1 

Copper      .... 

Cu2O 
CuO 

321 

585 

CuCl 
CuCl8 

52O 
8l9 

CuS 

rS8 

i 

« 

14 

593 

_ 

— 

— 

— 

4 

Hydrogen* 

H2O 

34J54 

HC1 

22OOO 

H2S 

2250 

3 

"         .... 

(i 

34800 

— 

— 

~ 

""~ 

5 

« 

U 

344  i  7 

_ 

— 

— 

— 

6 

Iron  

FeO 

1353 

FeCl2 

1464 

FeSH2O 

428 

3 

« 

— 

FeCl3 

1714 

— 

— 

3 

Iodine        .... 

I205 

177 

— 

— 

— 

— 

Lead          .         .         .         • 

PbO 

243 

PbCl2 

400 

PbS 

98 

Magnesium 
Manganese 
Mercury    .... 

MgO 
MnOH2O 
Hg20 
HgO 

6077 
1721 
105 
*53 

MgCl2 
MnCl2 
HgCl 
HgCl2 

6291 
2O42 
206 
3IO 

MgS 
MnSH2O2 

HgS 

3T9i 
841 

84 

Nitrogen* 

N2O 

-654 

- 

- 

— 

M 

NO 

—  i54i 

— 

— 

— 

— 

(( 

NO2 

—  143 

— 

- 

— 

— 

i 

Phosphorus  (red) 

P205 

5272 

- 

- 

- 

- 

i 

(yellow) 

u 

5747 

- 

— 

—  . 

— 

7 

«                   «« 

" 

5964 

— 

— 

— 

— 

i 

Potassium 

K2O 

1745 

KC1 

2705 

K2S 

1312 

8 

Silver         .... 

Ag20 

27 

AgCl 

271 

Ag2S 

24 

i 

Sodium      .... 

Na2O 

3293 

NaCl 

4243 

Na2S 

1900 

8 

Sulphur     .... 

S02 

2241 

- 

- 

- 

- 

i 

« 

tt 

2165 

— 

— 

— 

— 

2 

Tin    

SnO 

573 

SnCl2 

690 

_ 

— 

4 

SnCl4 

1089 

_ 

_ 

7 

Zinc  

ZnO 

1185 

- 

- 

4 

M 

u 

i3H 

ZnCl2 

H95 

~ 

" 

i 

Substance. 

Combined 
withS  +  O* 
to  form  — 

Heat 
units. 

Combined 
with  N  +  O3 
to  form  — 

Heat 

units. 

Combined 
withC  +  0, 
to  lorm  — 

Heat 

units. 

|  . 

<j-~ 

Calcium     .... 

CaSO4 

7997 

Ca(N03)2 

5080 

CaCO3 

6730 

Copper      .... 

CuSO4 

2887 

Cu(NO3)2 

I3°4 

— 

— 

Hydrogen 
Iron  

H2S04 
FeSO4 

96450 
4208 

HNO3 

Fe(N03)2 

41500 
2134 

: 

•     — 

Lead          .... 

PbSO4 

1047 

Pb(N03)2 

512 

PbC03 

8l4 

Magnesium 

MgS04 

12596 

_ 

- 

Mercury    .         .                 . 

— 

— 

— 

— 

— 

Potassium          .        . 

K2S04 

4416 

KN03 

3061 

K2CO3 

3583 

Silver         .... 

Ag2S04 

776 

AgN03 

266 

Ag2C03 

56l 

Sodium      .... 

Na2SO4 

7119 

NaNO3 

4834 

Na2C03 

5841 

Zinc  .        .         .        .     -    . 

ZnSO4 

3538 

— 

~ 

" 

AUTHORITIES. 

i  Thomsen.        3  Favre  and  Silbennann.     5  Hess.                                           7   Andrews. 

2  Berthelot.        4  Joule.                                   6  Average  of  seven  different.      8  Woods. 

SMITHSONIAN  TABLES. 


*  Combustion  at  constant  pressure. 
202 


COMBINATION. 


DUmbersindicate  *« 


TABLE  212. 


of  water,  in  the  same 


In  dilute  solutions. 

o 

Substance. 

Forms  — 

Heat 
units. 

Forms  — 

Heat 
units. 

Forms  — 

Heat 
units. 

•£  • 

Calcium 
Carbon  —  Diamond  . 

CaOH2O 

3734 

CaCl2H2O 

4690 

CaS  +  H2O 

2457 

I 

2 

"      —  Graphite   . 

I 

I 

~ 

— 

— 

- 

3 

Chlorine    . 

_ 

_  '  . 

3 

Copper 

H 

- 

- 

- 

- 

- 

_ 

i 

. 

~ 

— 

— 

— 

i 

Hydrogen  .         ... 

- 

- 

- 

- 

- 

: 

4 
3 

! 

_ 

_ 

I 

~ 

•• 

~ 

I 

Iron  ... 

FeO  +  H2O 

1  2  2O* 

FeCl2  4-  H2O 

1785 

_ 

_ 

3 

" 

— 

— 

FeCl8 

2280 

_ 

_ 

3 

Iodine 

_ 

_ 

_ 

_ 

•  _ 

_ 

Lead  .... 

.  _ 

_ 

PbCl2 

368 

_ 

Magnesium 
Manganese 

Mg02H2 

9°5°t 

MgCl2 
.   MnCl2 

7779 
2327 

MgS 

4784 

Mercury     . 

— 

— 

_ 

_ 

_ 

"           ... 

- 

— 

HgCl2 

299 

_ 

_ 

Nitrogen    . 

- 

- 

_ 

_ 

M 

- 

- 

- 

- 

- 

- 

Phosphorus  (red) 

_ 

_ 

_ 

: 

: 

: 

(yellow)  . 

- 

- 

- 

- 

- 

- 

7 

Potassium  . 

K2O 

2  1  10* 

KC1 

2592 

K2S 

1451 

8 

Silver 

— 

— 

— 

— 

i 

Sodium 

Na20 

3375 

NaCl 

4190 

Na2S 

2260 

8 

Sulphur 

- 

- 

- 

- 

- 

i 

"            ... 

— 

_ 

— 

_ 

_ 

— 

2 

Tin    . 

_ 

_ 

SnCl2 

691 

_ 

_ 

7 

" 

- 

- 

SnCl4 

1344 

- 

- 

7 

Zinc  .... 

— 

- 

— 

— 

— 

4 

«      .... 

— 

— 

ZnCl2 

1735 

— 

— 

i 

Substance. 

In  dilute  solutions. 

1=  >> 

Forms  — 

Heat 
units. 

Forms  — 

Heat 
units. 

Forms  — 

Heat 
units. 

Calcium 

- 

Ca(N03)2 

5'75 

_ 

_ 

Copper 
Hydrogen  . 
Iron  .... 

CuSO4 
H2SO4 
FeSO4 

3150 

105300 
42IO 

Cu(N03)2 
HNO, 
Fe(N03)8 

1310 
24556 
2134 

- 

- 

Lead  .... 

— 

Pb(N03)2 

475 

— 

— 

Magnesium 
Mercury     .         .         . 
Potassium  . 
Silver 
Sodium 
Zinc   .        .        ,.    ~    . 

MgS04 

K2SO4 
Ag2S04 
Na2SO4 
ZnSO4 

13420 
4324 

753 
7160 
3820 

Mg(N03)2 
Hg(N03)2 
KNO8 
AgNO3 
NaNO3 
Zn(N03)2 

8595 
335 
2860 
216 
4620 
2035 

Na2CO3 

5995 

AUTHORITIES. 

i  Thomsen.        3  Favre  and  Silbermann.      5  Hess.                                         7  Andrews. 
2  Berthelot.         4  Joule.                                   6  Average  of  seven  different.    8  U  oods. 

SMITHSONIAN  TABLES. 


*  Thomsen.  t  Total  heat  from  elements. 

203 


TABLE  213. 


LATENT   HEAT   OF   VAPORIZATION. 

The  temperature  of  vaporization  in  degrees  Centigrade  is  indicated  by  T  ;  the  latent  heat  in  calories  per  kilogramme 
or  in  therms  per  gramme  by  H ' ;  the  total  heat  from  o°  C.  in  the  same  units  by  H',  The  pressure  is  that  due  to 
the  vapor  at  the  temperature  T. 


Substance. 

Formula 

T 

H 

HI 

Authority. 

Acetic  acid     .... 

C2H4O2 

118° 

84.9 

- 

Ogier. 

Alcohol  :  Amyl 

CsHi2O 

!3i 

1  2O 

- 

Schall. 

Ethyl      . 

C2H60 

_ 

209 

_ 

Favre  and  Silbermann. 

« 
« 

« 
u 

78.1 

o 

9 

255 
236 

Wirtz. 
Regnault. 

M 

« 

5° 

264 

M 

« 

" 

IOO 

_ 

267 

" 

« 

" 

150 

- 

285 

M 

Methyl   . 

CH40 

64.5 

2.67 

3°7 

Wirtz. 

H 

" 

o 

289 

289 

Ramsay  and  Young. 

. 

" 

5° 

— 

274 

«                  "                      H 

"... 

M 

IOO 

_ 

246 

«                  «                      (( 

« 

« 

J5o 

_ 

206 

«                 <«                      (« 

« 

" 

200 

— 

X52 

<<                U                    « 

«« 

238.5 

- 

44-2 

«                «                    « 

Ammonia       .... 

NH3 

7-8 

294.2 

_ 

Regnault. 

. 

u 

ii 

291.3 

— 

H 

« 

<« 

16 

297.4 

_ 

(( 

tt 

it 

«7 

296.5 

- 

«< 

Benzene          . 

C6H6 

80.  i 

92.9 

127.9 

Wirtz. 

Bromine         .        .        ... 

Ba 

88 

45-6 

;- 

Andrews. 

Carbon  dioxide,  solid     . 
liquid  . 

«                       4<                     <t 

C02 

—25 

72.23 

138-7 

Favre. 
Cailletet  and  Mathias. 

M 

o 

57-48 

— 

"                     U                      <i 

«                       <(                     U 

II 

12.35 

44-97 

- 

Mathias. 

" 

22.04 

31.8 

— 

« 

«                      «                     « 

" 

29.85 

14.4 

_ 

« 

«                       «                     U 

(( 

30.82 

3-72 

- 

ii 

"      disulphide 
«             « 

CS2 

46.1 

83.8 

94-8 

Wirtz. 

«<             «« 

II 

o 

90 

90 

Regnault. 

«             <« 

IOO 

— 

100.5 

<« 

140 

— 

102.4 

" 

Chloroform    .... 

CHC13 

60.9 

58.5 

78.8 

Wirtz. 

Ether      .        ...... 

C4Hi00 

34-5 

88.4 

107 

« 

« 

34-9 

90-5 

Andrews. 

«                          ... 

^^ 

o 

94 

94 

Regnault. 

«< 

« 

50 

- 

115.1 

«< 

1  20 

~ 

140 

tt 

~ 

2-95 

- 

Favre  and  Silbermann. 

Sulphur  dioxide     . 

<<            « 

SO2 

o 

91.2 

_ 

Cailletet  and  Mathias. 

«            « 

3° 

80.5 

_ 

«          «          « 

II 

65 

68.4 

- 

«          «          <t 

Turpentine     .... 

CioHio 

159-3 

74.04 

_ 

Brix. 

Water    

H20 

« 

IOO 

535-9 

_ 

Andrews. 

ICO 

637 

Regnault. 

204 


LATENT    HEAT   OF   VAPORIZATION.* 


TABLE  213, 


Substance,  formula,  and 
temperature. 


=  total  heat  from  fluid  at  o°  to  vapor  at  P. 
r= latent  heat  at  P. 


Authority. 


Acetone, 
C3H60, 


Benzene, 


Carbon  dioxide, 

C02, 
—  25°  to  31°. 


Carbon  disulphide, 

CS2, 
—  6°  to  143°. 


Carbon  tetrachloride, 

ecu, 

8°  to  163°. 


Chloroform, 

CHClg, 

-5°  to  1 59°. 


Nitrous  oxide, 

N2O, 

—  20°  tO  36°. 


Sulphur  dioxide, 

S02, 
o°  to  60°. 


/=  140.5  +  0.36644  /  —  0.000516  ft 
1=  139-9  +  0.23356  /  -f  0.00055358  ft 
r=  139.9  —  0.27287  /  +  0.0001571 1'2 


1=  109.0  -f  0.24429 1  —  0.000131  S/2 


1 18.485  (31  —  t)  —  0.4707  (31  — 


0.14601  1  —  0.000412  ft 

/=  89.5  4-  0.16993  1  —  0.0010161  ft  +  0.000003424  fl 

r  =  89.5  —  0.06530  /  —  0.0010976  ft  -f-  0.000003424  /3 


/=  52.0  +  0.14625  t  —  0.000172  0 

/=  51.9  +  0.17867  t  —  0.0009599/2  +  0.000003733  1* 

r  —  51.9  —  0.01931  /  —  0.0010505  ft  +  0.000003733  /• 


. 

/= 67.0  4-  0.14716  /— 0.0000437  ft 

r  =  6j.o  —  0.08519  /  —  0.0001444  ft 


2=  131.75  (36.4  —  t)  —  0.928  (36.4  —  /)2 


r  =   91 .87  —  0.3842  f  —  0.000340  /2 


Regnault. 
Winkelmann. 


Regnault. 


Cailletet  and 
Mathias. 


Regnault. 
Winkelmann 


Regnault. 
Winkelmann 


Regnault. 
Winkelmann 


Cailletet  and 
Mathias. 


Mathias. 


*  Quoted  from  Landolt  and  Boernstein's  "  Phys.  Chem.  Tab."  p.  35°- 
SMITHSONIAN  TABLES. 


TABLE  214, 


LATENT  HEAT  OF  FUSION, 


This  table  contains  the  latent  heat  of  fusion  of  a  number  of  solid  substances.  It  has  been  compiled  principally  frorc 
Landolt  and  Boernstein's  tables.  C  indicates  the  composition,  T  the  temperature  Centigrade,  and  H  the  latent 
heat. 


Substance. 

C 

T 

H 

Authority. 

Alloys:  30.5?!)  4-  og^Sn  . 

PbSn4 

183 

I7 

Spring. 

36-9Pb  -j-  61.3811  . 
63.7  Pb  +  36.3811  . 

PbSns 
PbSn 

•79 

177-5 

15-5 

1  1.  6 

u 

77.8Pb-j-  22.280  . 

PbjSn 

176.5 

9-54 

" 

Britannia  metal,  9811  +  i  Pb 

— 

236 

28.0* 

Ledebur. 

Rose's  alloy, 

24Pb  -f-  27.380  +  48.76! 

- 

98.8 

6.85 

Mazzotto. 

Wood's  alloy  |  ^'ri^nt^Cd  | 

- 

75-5 

8.40 

« 

Bromine      

Br 

—7-32 

16.2 

Regnault. 

Bismuth      

Bi 

266.8 

12.64 

Person. 

Benzene      .         .         . 

CeH6 

5-3 

30.8? 

Fischer. 

Cd 

s-s 

Calcium  chloride 

CaCl2  +  6H2O 

328.'5 

40.7 

<4 

Iron,  Gray  cast  .... 

- 

23 

Gruner. 

White  "     . 

— 

_ 

33 

« 

Slag  

_ 

_ 

5° 

« 

Iodine         

I 

- 

11.71 

Favre  and  Silbermann. 

Ice      

H20 

o 

79.24 

Regnault. 

II 

" 

o 

80.02 

Bunsen. 

"     (from  sea-water) 

i      of  solids      ( 

-8.7 

54-o 

Petterson. 

Lead  

Pb 

31  C 

c  86 

I?     A\ 

Mercury      
Naphthalene       .... 
Palladium   
Phosphorus         .... 
Potassium  nitrate 

A 

v.,  jo  n  g 
Pd 
P 
KNO3 

-J 

79.87 

(  i  500)  ? 
40.05 
333-5 

5.00 
2.82 
35-62 
36.3 
4-97 
48.9 

ix  uciDerg. 
Person. 
Pickering. 
Violle. 
Petterson. 
Person. 

Phenol         

C^I'TcO 

1  A   ClI 

T)          .A 

Paraffin       

J\V 

4-yj 

j  cLicraon. 

. 

r\r\r\ 

35- 

ateiii. 

Sodium  nitrate   .... 

Narfo3 

999 
305-8 

21.07 
64-87 

i  erson. 

Sodium  phosphate 

(  NaoHPO4  ) 
(   +  I2H2O   } 

36-1 

66.8 

H 

Spermaceti          .... 
Sulphur       
Wax  (bees)         .        .        . 

8 

43-9 
TI5 
61.8 

36.98 

9-37 
42.1 

BateUi. 
Person. 
u 

Zinc    

Zn 

28  i  7 

(( 

415-3 

zo.  1  3 

SMITHSONIAN  TABLES. 


Total  heat  from  o°  C. 


206 


MELTING-POINT  OF  CHEMICAL   ELEMENTS.        T*BLE  215' 

»  - 


Range. 

Si 

Range. 

Substance. 

TW 

E 

£ 

Min. 

Max. 

1 

Substance. 

Min. 

Max. 

Mean. 

Aluminium  .     . 
Antimony     .     . 
Arsenic    . 
Barium    . 
Beryllium     .     . 
Bismuth  .     .     . 
Boron,  amorph. 
Bromine  .     .     . 
Cadmium     .     . 
Caesium  .     .     . 
Chlorine,  liquid 
Chromium   .     . 
Cobalt      .     .     . 

600. 

**& 

above 
below 
266.8 
melts 
—7.2 
3i5- 

above  t 
1500. 

C.° 
850. 
450. 
Sb  ant 
that  of  c 
that  of 
269.2 
in  elec 

—7-3 
321. 

lat  of  p 
1800. 

c.° 
625. 

435- 
lAg 
ast  iron 
silver 
268.1 
t.  arc 
—7.27 
318. 
26.5 

IO2. 

latinum 
1650. 

I 

2 

3 

4 

I 

7 

Lithium   .     .    . 
Magnesium  . 
Manganese  .     . 
Mercury  .     .     . 
Molybdenum    . 
Nickel     .     .     . 
Osmium  .    .     . 
Nitrogen      .     . 
Palladium     .    . 
Phosphorus 
Platinum      .     . 
Potassium    .     . 
Rhodium      .     . 

C.° 

750- 

-38.5C 
abov 
1450. 

-203. 

1350. 
44.2 

1775- 
55- 

C.u 

800. 

—39-44 
e  white 
1600. 

—214. 
1950. 
44-4 

22OO. 
63. 

180. 

775- 
1900. 

—39-04 
heat 
1500. 
2500. 
—208. 
1600. 
44.25 
1900. 
60. 

2OOO. 

13 
13 

M 

IS 

16 
16 

Copper    .     .     . 

1050. 

I33°- 

IIOO. 

Rubidium    .    . 

_ 

_ 

18.  q 

Gallium  . 

— 

3°-  T  5 

8 

Ruthenium  .     . 

1800 

Germanium 

- 

- 

900. 

9 

Silenium  .     .     . 

_ 

217. 

17 

Gold    .... 

1035- 

1250. 

1080. 

Silicon     .     .     . 

bet.  cast  iron  a 

nd  steel 

7 

Indium     .     .     . 
Iodine 
Iridium   .     .     . 

107. 
1950. 

"5- 

TWO. 

176. 

112. 

2225. 

10 

Silver.    .    .    . 
Sodium    .     .     . 
Strontium    .    . 

916. 
95-6 

i 

IO4O. 
—97.6 

red  heat 

95°- 
97.6 

18 

Iron  (pure)  .     . 

1500. 

1800. 

l635- 

Sulphur  .     .    . 

III. 

1  20. 

1  1  5.1 

"     (white  pig) 

1050. 

IIOO. 

1075- 

Tellurium    .    . 

452. 

525- 

470. 

"    (g^y  pig) 

IIOO. 

2275. 

1  200. 

Thallium      .     . 

288. 

290. 

289. 

Steel    .... 

1300. 

1400. 

1360. 

Tin      ...... 

226.5 

235- 

230. 

"     (cast)  .     . 
Lanthanum  .     . 

betwee 

>n  Sb  ar 

,'375- 
d  Ag 

ii 

12 

Tungsten     .    ab 
Zinc    .... 

ove  that 
400. 

of  man 
433- 

ganese 
4i5- 

19 

Lead   .... 

322. 

335- 

326. 

1  Mallet.                   6  Olszewski,  1884.     10  Winkler,  1867.        u  Carnelley,  1879. 

2  Frey.                      7  Deville,  1856.         n  Ledebur,  1881.        16  Buchholz.             w  Wohler. 

8  Debray.                  8  Lecoq  de  Bois-      12  Hildebrand  and      16  Pictet,  1879. 

4  Despretz.                      baudran,  1876.           Norton,  1875.         n  Hittorf,  1851. 

6  Setterberg,  1882.    9  Winkler,  1886.       13  Bunsen.                    18  Matthieson,  1855. 

BOILING-POINT   OF   CHEMICAL    ELEMENTS. 


TABLE  216. 


The  column  headed  "  Range  "  gives  the  extremes  of  the  records  found.     Where  the  results  are  from  one  observer 
the  authority  is  quoted  with  date  of  publication. 


Range. 

1 

Range. 

f 

Substance. 

Mean. 

Substance. 

Mean. 

I 

Min. 

Max. 

° 

Min. 

Max. 

$ 

Aluminium  .     . 

abov 

e  white 

heat 

i 

Nitrogen  .     .    . 

_ 

_ 

—194.4 

8 

Antimony    .     . 
Arsenic    . 

1470. 
449- 

1700. 
450. 

1535- 

2 

Oxygen    .     .     . 
Ozone.     .     .     . 

—  181. 

-184- 

—  1  06. 

9 

Bismuth  .     .     . 

1090. 

1700. 

1413- 

Phosphorus 

287.3 

290. 

288. 

Bromine  .     .     . 

59.27 

63.05 

62.08 

Potassium    .     . 

667. 

725. 

695. 

Cadmium     .     . 

720. 

860. 

779- 

Selenium 

664. 

683. 

675. 

Chlorine  .     .     . 

_ 

-^-6 

3 

Sodium    .     .    . 

742. 

907. 

825. 

Iodine 

over  200° 

4 

Sulphur  .     .     . 

447- 

448.4 

448.1 

Lead    .... 
Magnesium  . 
Mercury  .     .     . 

bet.  14 

50°  anc 

1600° 

IIOO. 

357- 

I 

7 

Thallium  .     .     . 
Tin      .... 
Zinc     .... 

1600. 
bet.  14 
891. 

1800. 
50°  and 
1040. 

1700. 
1600° 
958. 

i  Deville,  1854.   3  Regnault,  1863.  6  Carnellev,  1879.  T  Regnault,  1862.     •  Olszewski,  1887. 
2  Conechy.          *  Stas,  1865.           6  Ditte,  1871.          8  Olszewski,  1884. 

SMITHSONIAN  TABLES. 


207 


TABLE  217. 

MELTING-POINTS  OF  VARIOUS  INORGANIC  COMPOUNDS. 


Melting-points. 

>, 

Substance. 

Chemical  formula. 

Min. 

Max. 

'articular 
or  average 

o 

Date  of 
publication. 

values. 

^ 

Aluminium  chloride  . 

A1C13 

- 

- 

190. 

I 

1888 

"          nitrate    . 

A1(NO3)3  -}-  9H2O 

~ 

~ 

72.0 

' 

ft 

Ammonia  . 
Ammonium  nitrate   . 
"           sulphate 
"           phosphite 
Antimonietted  hydrogen  . 
Antimony  trichloride 
"          pentachloride   . 
Arsenic  trichloride    . 

NH3 
(NH4)N03 
(NH4)2S04 
NH4H2P08 
SbH3 
SbClg 
SbCl5 
AsCls 

145- 

72. 

1  66. 
73-2 

140. 
123. 

~72'.8 
—6. 
—  18. 

3 

4 

I 

1837 
1887 
1886 

1875 
1889 

Arsenietted  hydrogen 
Barium  chlorate 

AsH3 
Ba(C103)2 

""* 

_ 

—II3-5 
414. 

6 
9 

1878 

O       O 

"       nitrate 

Ba(N03)2 

— 

— 

593- 

9 

1878 

"       perchlorate  . 
Bismuth  trichloride  . 
Boric  acid 

Ba(C104)2 
BiCl3 
H3BO3 

225. 
184. 

230. 
1  86. 

5°5- 
227.5 
185. 

10 
ii 
9 

1884 
1876 
l878 

rt     r» 

"     anhydride 
Borax  (sodium  borate) 
Cadmium  chloride    . 

B203 
Na2B4O7 
CdCl2 

- 

- 

577- 
561. 
541. 

9 
9 
9 

1878 
1878 
1878 

"          nitrate 

Cd(NO3)2  4-  4H2O 

— 

— 

59-5 

2 

1859 

Calcium  chloride 

CaCl2 

719. 

723- 

72J' 

9 

1878 

"               " 

CaCl2  +  6H2O 

28. 

29. 

28.5 

— 

— 

"         nitrate 

Ca(NO3)2 

- 

561. 

9 

1878 

"             "              . 

Ca(N03)2  +  4H20 

- 

- 

44. 

2 

^59 

Carbon  tetrachloride         i 

CC14 

— 

— 

—24.7 

12 

1863 

"       trichloride    . 

C2C16 

182. 

187. 

184.5 

— 

— 

"       monoxide 

CO 

—199. 

—207. 

203. 

- 

- 

"       dioxide 

CO2 

-56.5 

-57-5 

—57- 

3 

J845 

"       disulphide    . 
Chloric  acid 

CS2 
HC1O4  +  H2O 

_ 

—  1  10. 

'3 
H 

1883 
1861 

Chlorine  dioxide 

C1O2 

— 

— 

-76. 

3 

1845 

Chrome  alum    . 

KCr(SO4)2-f  i2H2O 

- 

- 

89. 

15 

1884 

Chrome  nitrate 

Cr2(NO3)6  +  i8H2O 

— 

— 

37- 

2 

1859 

Cobalt  sulphate 

CoSO4 

96. 

98. 

97. 

15 

1884 

Cupric  chloride 

CuCl2 

- 

- 

498. 

9 

1878 

O      O 

Cuprous      "              ,        . 

Cu2Cl2 

— 

— 

434- 

9 

1878 

"        nitrate 

Cu(NO3)2  -|-  2H2O 

- 

- 

2 

1859 

Hydrobromic  acid     . 
Hydrochloric  acid     . 
Hydrofluoric  acid 

HBr 
HC1 
HF1 

- 

- 

—  112.5 
—92-3 

6 

1845 
1884 
1886 

Hydroiodic  acid 
Hydrogen  peroxide  . 
"         phosphide 

HI 
H202 
PH3 

- 

- 

—49-5 

ON  O\O.» 

1845 
1818 
1886 

"          sulphide   . 

H2S 

- 

- 

—  85.6 

3 

1845 

Iron  chloride     . 

FeCls 

301. 

3°7- 

3°3- 

- 

— 

"     nitrate 

Fe(N03)3  +  9H20 

47.2 

2 

1859 

"     sulphate     . 

FeSO4  +  7H2O 

— 

— 

64. 

15 

1884 

Lead  chloride    . 

PbCl2 

498. 

580. 

326. 

— 

"     metaphosphate 
Magnesium  chloride 

Pb(P03)2 
MgCl2 

800. 
708. 

9 
9 

1878 
1878 

nitrate    . 

Mg(NO3)2  +  6H2O 

— 

— 

90. 

2 

1859 

"            sulphate 

MgSO4  +  5H2O 

— 

— 

54- 

IS 

1884 

Manganese  chloride  . 

MnCl2  +  4H2O 

_ 

— 

87.$ 

17 

— 

nitrate    . 

Mn(NO3)2  +  6H2O 

_ 

— 

25.8 

2 

1839 

"           sulphate. 

MnSO4  +  5H2O 

_ 

_ 

54- 

I  e 

1884 

Mercuric  chloride 

HgCl2 

287. 

293- 

290. 

— 

~ 

i  Friedel  and  Crafts.      5  Amat.                 9  Carnelley.                            13  Wroblewski  and  Olszewski. 

2  Ordway.                        6  Olszewski.        10  Carnelley  and  O'Shea.      14  Roscoe. 
3  Faraday.                       7  Kammerer.      n  Muir.                                   15  Tilden.         17  Clark,  "  Const,  of  Nat." 

4  Marchand.                    8  Besson.            12  Regnault.                            16  The"nard. 

*  For  more  extensive  tables  on  this  subject,  see  Carnelley's  "  Melting  and  Boiling-point  Tables,"  or  Landolt  and 
Boernstein's  "  Phys.  Chem.  Tab." 


SMITHSONIAN  TABLES. 


20S 


TABLE  217, 
MELTING-POINTS  OF   VARIOUS   INORGANIC  COMPOUNDS. 


Melting-point. 

Substance. 

Chemical  formula. 

Particulai 

'§ 

Date  of  pub- 

Min. 

Max. 

or 

•=• 

lication. 

probabl 

's 

value. 

**« 

Nickel  carbonyl 
"      nitrate 
"      sulphate 
Nitric  acid  . 
"      anhydride 

NiCO4 
Ni(NO3)2  4-  6H2O 
NiSO4  4-  7H2O 
HNO3 

98. 

100. 

56.7 
99. 

—47- 

I 

2 

3 
4 

1890 

1859 
1884 
1878 

"      oxide  * 

NTY 

~ 

• 

30. 

1872 

"     peroxide 

i\  U 

** 

— 

-16.7 

6 

1885 

Nitrous  anhydride 
"        oxide 

N203 

- 

- 

—  10.1^ 
—82. 

• 

Is&J 

Phosphoric  acid  (ortho) 
Phosphorous  acid 
Phosphorus  trichloride 
oxychloride 
disulphide 
pentasulphide 
sesquisulphide 
trisulphide 
Potassium  carbonate   . 
chlorate 
perchlorate 
chloride 
nitrate 
acid  phosphate  . 
acid  sulphate 
Silver  chloride    . 
"      nitrate 
"      nitrogenietted   . 
perchlorate 
"      phosphate 
"      metaphosphate 
"       sulphate    . 
Sodium  chloride  . 
"       hydroxide 

H3P04 
H3P03 
PC13 
PC1O3 
PS2 
P2S5       i 
P4S3 
P2S3 
K2C03 
KC103 
KC1O4 
KC1 
KN03 
KH2P04 
KHS04 
AgCl 
AgN03 
AgN3 
AgC104 
Ag3P04 
AgP03 
Ag2S04 
NaCl 
NaOH 

38.6 
70.1 

296. 

274. 
142. 

834. 

334- 

730. 
327. 

45°- 
198. 

772. 

41.7 

74- 

298. 
276. 
167. 

1150.  ? 
372. 

738. 
353- 

457- 
224. 

960. 

—99. 

40-3 
72. 
1  1  1.8 

297. 

275- 
158. 
290. 
836. 

354- 
610. 

734- 
340. 
96. 

200. 

453- 
214. 
250. 
486. 
849. 
482. 
654. 

772- 
60. 

9 

10 

ii 

12 

I  L 

15 

16 

20 
18 
15 
15 

17 

1873 

1883 
1871 
1879 
1879 

1864 
1880 

1884 
1840 

1890 
1884 
1878 
1878 
1878 

1884 

"       nitrate 

NaNO3 

298. 

330. 

I1  "J. 

"       chlorate  . 

NaClO3 

~Q2 

j» 

1878 

"      perchlorate 

NaClO4 

_ 

_ 

482. 

18 

1884 

"       carbonate 

Na2CO3 

814. 

920. 

884. 

_ 

*  w*-/*t 

«                   a 

Na2CO3  4-  ioH2O 

-i 

1884 

"      phosphate 
"      metaphosphate 

Na2HPO4  4-  4H2O 
NaPO3 

35- 

36-4 

35-4 
617. 

o 
15 

j  V^T. 

1878 

pyrophosphate 

Na4P207 

_ 

_ 

888. 

15 

1878 

"       phosphite 

(H2NaPO3)2  4-  5H2O 

_ 

_ 

42. 

9 

1888 

sulphate  . 

Na2SO4 

861. 

865. 

863. 

5 

1878 

"         .        .  '  -'- 

Na2SO44-  ioH2O 

_ 

34. 

3 

1884 

"      hyposulphite   . 
Sulphur  dioxide  .        .. 

Na2S2034-5H20 
SO2 

76! 

48.1 
79- 

47- 
78. 

Sulphuric  acid     . 

H2S04 

IO.I 

10.6 

10.4 

21 

1884 

«<          « 

I2H2S04  4-  H2O 

_ 

_ 

—  °-5 

2 

" 

H2SO4  -f  H2O 

7-5 

8-5 

8.' 

_ 

_ 

Sulphur  trioxide 

H2S2O7 
SO3 

14.8 

35- 
14.9 

2 

5 

l853 
1876-1886 

Tin,  stannic  chloride  .  ! 

SnCl4 

— 

_ 

—33- 

3 

1889 

"     stannous     "         r 

SnCl2 

_ 

_ 

250. 

4 

Zinc  chloride 

ZnCl2 

_ 

_ 

262. 

5 

1875 

"         "                *        . 

ZnCl2  4-  3H2O 

_ 

_ 

7. 

6 

1886 

"     nitrate 

Zn(NO3)2  4-  6H2O 

_ 

_ 

36.4 

3 

1884 

"    sulphate 

ZnSO4  4-  7H20 

- 

- 

3 

1884 

i  Mond,  Langer  &  Quincke.     10  Wroblewski  &  Olszewski.    15  Carnelley.          20  Curtius.                25  Braun. 

2  Ordway.            6  Olszewski.     n  Genther  &  Michaelis.          16  Mitscherlich.     21  Mendelejeff.         26  Engel. 

3  Tilden.               7  Ramsay.         12  Ramme.                                   17  Cripps.                22  Maricnac. 

4  Berthelot.         8  Birhaus.         13  V.  &  C.  Meyer.        18  Carnelley  &O'Shea.      23  Benson. 

5  R.  Weber.        9  Wills.             14  Lemoine.     '                          19  Amat.                24  Clark,  "  Const,  of  Nat." 

SMITHSONIAN  TABLES. 


*  Under  pressure  138  mm.  mercury. 
2O9 


TABLE  218. 


BOILING-POINTS   OF   INORGANIC   COMPOUNDS.* 


F 

Boiling-point. 

£ 

Substance. 

Chemical  formula. 

Min. 

Max. 

Particular 
or  aver- 

| 

Date  of 

publication. 

age  values. 

* 

Airt    

_ 

_ 

_ 

—  192.2 

I 

1884 

_ 

_ 

— 

—  I9I.4 

2 

1884 

Aluminium  chloridej  . 

A1C13 

- 

- 

207.5 

3 

1888 

"           nitrate 

A1(NO3)3  +  9H2O 

- 

- 

134. 

4 

1859 

Ammonia    .         .        •  .•••, 

NH3 

— 

— 

-38.5 

5 

1863 

Antimonietted  hydrogen     . 
Antimony  pentachloride  §  . 

SbH3 
SbCl6 

IO2. 

I03. 

—  1  8. 

2 

6 

1886 
1889 

"          trichloride  . 

SbCl3 

216. 

223.5 

220. 

- 

— 

Bismuth  trichloride     . 

BiCl3 

427. 

441. 

435- 

5»  7 

— 

Cadmium  chloride      .        . 

CdCl2 

861. 

954- 

908. 

10 

1880 

"         nitrate 

Cd(NO3)2  +  4H2O 

- 

132. 

4 

1859 

Calcium  nitrate  . 

Ca(NO3)2  -j-  4H2O 

— 

— 

132. 

4 

1859 

Carbon  dioxide   .         ... 

C02 

—78.2 

—80. 

—79.1 

— 

1863-1880 

"       disulphide 

CS2 

46. 

474 

46.6 

8,9 

1880-1883 

"        monoxide 

CO 

190. 

—193- 

—  191.5 

2,  I 

1884 

Chromic  oxychloride  . 
Chromium  nitrate 

CrO2Cl2 
Cr2(N03)6  +  i8H20 

"5-9 

118. 

117. 
125.5 

4 

1859 

Copper  nitrate     . 

Cu(NO3)2  -f  3H2O 

- 

- 

170. 

4 

1859 

Cuprous  chloride    "    . 

Cu2Cl2 

954- 

1032. 

993- 

10 

1880 

Hydrobromic  acid  ||    . 

HBr 

125. 

125-5 

ii 

1870 

Hydrochloric  acid 

HC1 

no. 

12 

1859 

Hydrofluoric  acid 

HF 

125. 

I25-5 

- 

13 

1869 

Hydroiodic  acid  . 

HI 

— 

127. 

II 

1870 

Iron  nitrate 

Fe(N03)3  +  9H20 

- 

- 

125. 

4 

1859 

Magnesium  nitrate 
Manganese  chloride    . 

Mg(N03)2  +  6H20 
MnCl2  +  4H2O 

— 

: 

143- 
1  06. 

4 
14 

1859 

"           nitrate 

Mn(NO3)2  +  6H2O 

- 

- 

129.5 

4 

1859 

Mercuric  chloride 

HgCl2 

502. 

307- 

3°4- 

— 

Nickel  nitrate 

Ni(NO3)2  +  6H2O 

136.7 

4 

1859 

Nitric  acid  .... 

HN08 

_ 

— 

86. 

15 

l830 

"      anhydride 

N205 

45- 

5°- 

- 

16 

1849 

"      oxide 

NO 

— 

—  153. 

2 

I885 

Nitrous  anhydride 

N203 

—  10. 

3-5 

_ 

— 

"        oxide 

N2O 

-87.9 

—92. 

—92. 

- 

- 

Phosphorus  trichloride 

PC13 

73-8 

76. 

75- 

— 

- 

"            sesquisulphide 

P4S3 

380. 

17 

1883 

trisulphide 

P2S3 

_ 

_ 

49°. 

17 

1886 

pentasulphide 

P2S5 

518. 

530- 

522. 

- 

"           trioxide   . 

P208 

is 

1890 

Silicon  chloride  . 

SiCl4 

56.8 

59- 

'sS3' 

_ 

_ 

Sulphuric  acid     .        .     •    , 

I2H2SO4  +  H2O 

_ 

338. 

19 

1853 

Sulphur  trioxide 

SO3 

46. 

47- 

46-3 

_ 

"        dioxide  .        .        . 

S02 

—8. 

—10.5 

-9-6 

_ 

_ 

"        chloride      *   . 

S2C12 

138. 

144. 

_ 

_ 

Tin,  stannous  chloride 

SnCl2 

606. 

628. 

617.' 

_ 

_ 

"    stannic          " 

SnCl4 

_ 

_ 

11  3-9 

8 

1876 

Zinc  chloride 

ZnCl2 

676. 

73°- 

703- 

- 

- 

"    nitrate 

Zn(NO3)2  +  6H2O 

— 

4 

I859 

i  Wroblewski.                      8  Thorpe.                                                  15  Mitscherlich. 

2  Olszewski.                          9  Friedburg.                                                16  Deville. 

3  Friedel  and  Crafts.          10  Carnelley  and  Carleton-  Williams.        17  Isambert. 

4  Ordway.                            11  Topsoe.                                                    18  Thorpe  and  Tutton. 

5  Regnault                          12  Roscoe  and  Dittmar.                             19  Marignac. 
6  Anschiitz  and  Evans.      13  Gore. 

7  Pictet.                               14  Clark,  "Const,  of  Nature." 

*  For  a  more  complete  table,  see  Clark's  "  Constants  of  Nature''  (Smithsonian  Collections). 

t  Pressure  76  cm.  i  Pressure  2.64  atmos.  §  Pressure  68  mm.  ||    Pressure  75.8  cm. 


SMITHSONIAN   TABLES. 


2IO 


MELTING-POINTS  OF  MIXTURES.* 


TABLE  219, 


Metals 
and 
observe 

Atomi 
ratio. 

Per  cent 
of  metal. 

Per  cent 
of  metal. 

M 

Metals 
and 
observe 

Atomic 
ratio. 

Per  cent 
of  metal,  j 

Per  cent 
of  metal.  1 

Percent 
of  metal.  1 

C   p 

P 

Pb 
and 

Pb4Sn 
PbgSn 
Pb2Si 
PbSn 
PbSn 

Pb 

Sn 
I2.C 

16.0 

22.2 

36.3 
C-I.' 

292. 

283. 

270. 
235- 

1  07 

Cd,Sn 
Pb 
and 

Cd4SngPb5Bii 
Cd3Sn4Pb4Bi 
CdSn2Pb2Bi4 
CdSnPbBi 

Cd 

10.8 

IO— 

7.0 

Sn 

14.2 

14-3 
14-8 
13.8 

Pb 

24.9 

24-3 

Bi 

50- 
50-4 

65.5 
67.5 
68.5 
68.1 

PbSn3 

54 

63.? 

181! 

PbSn4 

30.5 

69.5 

187. 

Cd 

Pb 

Bi 

Pb 
and 

Pb3Bi 

Pb 

27.2 

Bi 

Cd,  Pb 
andBi 

CdPb3Bi4 
Cd2Pb7Bi8 

39-7 
43-4 

53-2 
49-9 

- 

89.5 
95-o 

Bi2 

' 

Cd 
and 

CdBi4 

Cd 

21.2 

Bi 
78.8 

146.3 

Sn,  Pb 
and  Bi 

- 

Sn 

as 

Pb 
25.0 
31.2 

Bi 
50.0 
50.0 

- 

95-o 
95-o 

Cd 
and 
Sn2 

CdSn2 

Cd 

32.2 

Sn 
67.8 

173-8 

Zn,  Pb 

and  Sn 

- 

Zn 

4.2 

Pb 

26.9 

Sn 
68.9 

- 

168. 

Sn 

Sn3Bi4 

Sn 

Bi 

and 
Bi2 

- 

29.8 

70.2 

136-4 

Cu  and 
Zn 

Cu 

Zn 

7n 

Ph 

(white 

— 

50.0 

50.0 

- 

- 

912. 

Zn 

- 

l-t\\ 

83.3 

1   L) 

!6.7 

205. 

brass)  9 

and 

- 

69-5 

3°-5 

190. 

Ag 

Au 

Pb3 

— 

5O.O 

50.0 

202. 

- 

100. 

- 

- 

954- 

Zn 

and 
Sb3 

: 

Zn 

£ 

Sb 

IO. 

1  8. 

236. 
250. 

and 
Au10 

- 

80. 
60. 
40. 
20. 

20. 
40. 
60. 
80. 

- 

- 

975- 
995- 
1  020. 
1045. 

— 

— 

IOO. 

_ 

_ 

[O7  s 

Pb 

Pb 

Sb 

3,11  d 

— 

90. 

IO. 

240. 

Sb3 

- 

82. 

18. 

260. 

Au 

Pt 

— 

100. 

- 

- 

- 

1075. 

— 

95- 

5. 

— 

_ 

I  IOO. 

Na 

Na 

K 

_ 

QO. 

IO. 

_ 

_ 

I  ->Q, 

and 

- 

50. 

50- 

6. 

- 

^r~" 
85- 

_ 

_ 

1160. 

K4 

— 

80. 

20. 

_ 

1190. 

Ag 

Cu 

- 

75- 

25- 

- 

- 

1220. 

— 

IOO. 

— 

040. 

— 

70. 

— 

- 

255- 

— 

92-5 

7-5 

931.0 

— 

65. 

35- 

- 

— 

285. 

— 

17.9 

86.0 

— 

60. 

40. 

_ 

_ 

320. 

— 

79-8 

20.2 

87.0 

Au 

_ 

55- 

45. 

_ 

_ 

35°. 

- 

77-4 

22.6 

58.0 

and 

- 

_ 

_ 

385- 

- 

75-o 

25.0 

50.0 

Pt8 

- 

45- 

55- 

- 

- 

420. 

Ag 

— 

71.9 

28.1 

70-5 

— 

40. 

60. 

— 

_ 

460.  ! 

and 

- 

63.0 

37-o 

47.0 

- 

35- 

65. 

- 

- 

495- 

Cu5 

— 

60.0 

40.0 

57-o 

- 

3°- 

70. 

- 

- 

535- 

— 

57-0 

43-° 

oo.o 

— 

25- 

75- 

— 

- 

570. 

— 

54-i 

45-9 

2O.O 

— 

20. 

80. 

— 

— 

610. 

- 

50.0 

50.0 

4I.O 

- 

15. 

85. 

- 

- 

6qo. 

- 

45-9 

54-  r 

61.0 

- 

IO. 

90. 

- 

- 

690.  i 

— 

25.0 

75-o 

114. 

— 

5. 

95- 

— 

— 

730- 

— 

— 

00. 

33°- 

— 

— 

oo. 

— 

— 

775- 

. 

i  Pillichody,  "  Ding.  Poly.  Jour."  vol.  162.                                6  Von  Hauer,  "  J.  f.  prakt.  Ch."  (i),  94,  436. 
2  Rudberg,  "  Pogg.  Ann.':  71.                                                        7  W.  Spring,  "  Fort.  d.  Phvs."  1875. 
3    Ledebur,  "  Wied.  Bieb."  5,  650,  1881.                                       8  Svanberg,  "  J.  B.  f.  Ch/'  1847-48. 
4  Rosenfeld,  "  Ber.  Chem.  Ges."  1891.                                        g  Daniell,  Bolley's  "  Hdb.  f.  ch.  Techn/;  8,  45. 

5  W.  Roberts,  "Ann.  Chem.  et  Phys."  (5),  13,  118,  1878.       10  Erhard  and  Schutel,  "  Fort.  d.  Phys."  vol.  35. 

SMITHSONIAN  TABLES. 


From  Landolt  and  Boernstein's  "  Phys.  Chem.  Tab.3 
211 


TABLE  22O, 


DENSITIES,    MELTING-POINTS,   AND    BOILING-POINTS  OF   SOME 
ORGANIC  COMPOUNDS. 

N.  B.  —  The  data  in  this  table  refer  only  to  normal  compounds. 


Substance. 

Formula. 

Temp. 

Den- 
sity. 

Melting- 
point. 

Boiling-point. 

Authority. 

(a)  Paraffin  Series:  CwH2W_j_2. 

Methane*    .     .     . 

CH4 

—  164. 

0.415 

—185.8 

—  164. 

Olszewski. 

Ethanet  .... 
Propane  .... 
i  J^ut^inc         •     •     • 

C2H6 
C3H8 

O 

.60 

- 

—25  to  —30 

Roscoe  and  Schorlemmer. 
Butlerow. 

Pentane  .... 

C5Hi2 

17- 

.626 

- 

+37- 

Schorlemmer. 

Hexane  .... 

CeHi4 

17- 

•663 

- 

-(-69. 

it 

Heptane  .... 

C7Hie 

O 

.701 

- 

98.4 

Thorpe. 

Octane    .... 

C8Hi8 

O 

.719 

— 

125-5 

" 

Nonane  .... 

CgH20 

20. 

.718 

—  51- 

150. 

Krafft. 

Decane   .... 

CioH22 

2O. 

•73° 

—  31- 

173- 

Undecane    .     .     . 

CliH24 

—26. 

•774 

—26. 

195- 

" 

Dodecane    .     .     . 

C  12^126 

—  12. 

•773 

—  12. 

214. 

H 

Tridecane    .     .     . 

C13H28 

—6. 

•775 

—6. 

234- 

" 

Tetradecane     .     . 

C14H3o 

+4- 

+4- 

252. 

" 

Pentadecane    .     . 

Cisrl32 

IO. 

.776 

+  10. 

270. 

" 

Hexadecane     .     . 

CieH34 

18. 

•775 

18. 

287. 

II 

Heptadecane   .     - 

Ci7H3e 

22. 

•777 

22. 

303- 

" 

Octadecane  .     .     . 

Ci8H38 

28. 

•777 

28. 

317. 

" 

Nonadecane     .     . 

CigH40 

32- 

•777 

32- 

33°- 

(i 

Eicosane 

C2oH42 

37- 

•778 

37- 

2054 

ft 

Heneicosane    .     . 

C2iH44 

40. 

.778 

40. 

2154 

11 

Docosane     .     .     . 

C22H46 

44- 

.778 

44- 

2244 

U 

Tricosane    .     .     . 

48. 

•779 

48. 

2344 

U 

Tetracosane     .     . 

C24H50 

51- 

•779 

51- 

2434 

" 

Heptacosane    .     . 

C27H56 

60. 

.780 

60. 

2704 

fl 

Pentriacontane     . 

C3iHe4 

68. 

.781 

68. 

3024 

" 

Dicetyl    .... 

C32H66 

70. 

.781 

70. 

3r°4 

" 

Penta-tria-contane 

C35H72 

75- 

.782 

75- 

33i4 

(b)  defines,  or  the  Ethylene  Series:  CWH2W. 

Ethylene      .     .     . 

C2H4 

_ 

_ 

-169." 

—103. 

Wroblewski  or  Olszewski. 

Propylene    .     .     . 

C3H6 

— 

— 

Butylene      .     .     . 
Amylone      .     .     . 
Hexylene     .     .     . 

C4H8 

—  13-5 

0 

0'635 
.76 

- 

1 

Sieben. 
Wagner  or  Saytzeff. 
Wreden  or  Znatowicz. 

Heptylene   .     .     . 

C7Hu 

19.5 

•703 

- 

96.-99. 

Morgan  or  Schorlemmer. 

Octylene      .     .     . 

C8H16 

17. 

.722 

— 

I22.-I23. 

Moslinger. 

Nonylene     .     .     . 

CgHi8 

— 

_ 

I53- 

Bernthsen,  "  Org.  Chem." 

Decylene     .     .     . 
Undecylene      .     . 

CnlS 

— 

: 

— 

175- 

«                          H       •         i! 

Dodecylene      .     . 

Ci2H24 

—31- 

•795 

—3i- 

964 

Krafft. 

Tridecylene      .     . 

Cj3H26 

233- 

Bernthsen. 

Tetradecylene  .     . 

CuH28 

—  12. 

•794 

—  12. 

1274 

Krafft. 

Pentadecylene 

Ci5H3o 

_ 

_ 

247. 

Bernthsen. 

Hexadecylene  .     . 
Octadecylene   . 

ci8H33e 

+4- 
18. 

•792 
.791 

+4- 
+  18. 

1554 
1794 

Krafft,  Mendelejeff,  etc. 
Krafft. 

Eieosylene  .     .     . 

C2oH4Q 

— 

Cerotene      .     .     . 

C27H54 

- 

_ 

58- 

_ 

Bernthsen. 

Melene    .... 

C30H6o 

~ 

62. 

"* 

*  Liquid  at  —  n.°  C.  and  180  atmospheres'  pressure  (Cailletet). 

+  4-°  46          "  "  " 

T  Boiling-point  under  15  mm.  pressure. 


SMITHSONIAN  TABLES. 


212 


TABLE  22O 

DENSITIES,   MELTING-POINTS,   AND   BOILING-POINTS   OF   SOME 
ORGANIC   COMPOUNDS. 


Substance. 

Chemical 
formula. 

Temp. 

Specific 
gravity. 

Melting- 
point. 

Boiling- 
point. 

Authority. 

(C)  Acetylene  Series  :  CWH2M_2. 

Acetylene  . 

C  H 

Allylene      

£2TT2 

~ 

~ 

Ethylacetylene    .     .     . 

C4H6 

- 

- 

_ 

+  18. 

Bruylants,  Kutsche- 

Propylacetylene       .     . 
Butylacetylene          .     . 
Oenanthylidene        .     . 

C6H8 
Cflfo 

liSU, 

- 

- 

48.-50. 
68.-70. 
io6.-io8. 

roff,  and  others. 
Bruylants,  Taworski. 
Taworski. 
Bruylants,  Behal, 

Caprylidene    .          .     . 
Undecylidene.          .     . 
Dodecylidene           .     . 
Tetradecylidene       .     . 
Hexadecylidene       .     . 

C8H14 

Ci2H22 
CUH26 

0. 

its 

20. 

0.771 

.810 
.806 
.804 

2O. 

I33--I34- 

2IO.-2I5- 
105.* 

1  60!* 

Behal. 
Bruylants. 
Krafft. 

Octadecylidene         .     . 

Ci8H34 

30- 

.802 

30- 

184.* 

" 

(d)  Monatomic  alcohols  :  CnU.2n  \  tOH. 

Methyl  alcohol 

CHgOH 

0. 

0.8  1  2 

_ 

66. 

Ethyl  alcohol  . 

C2H5OH 

0. 

.806 

—I30.t 

78. 

Propyl  alcohol 

C3H7OH 

o. 

.817 

97- 

From  Zander,  "  Lieb. 

Butyl  alcohol  . 
Amyl  alcohol  . 

C4H9OH 
C5HnOH 

o. 
o. 

.823 

.829 

- 

117. 
138. 

Ann."  vol.  224^.85, 
and  Krafft,  "Ber." 

Hexyl  alcohol 

C6H18OH 

0. 

•833 

_ 

J57- 

vol.  16,  1714, 

Heptyl  alcohol 

C7H15OH 

0. 

.836 

_ 

176. 

"    19,  2221, 

Octyl  alcohol  . 

C8H17OH 

0. 

•839 

_ 

"    23,  2360, 

Nonyl  alcohol 

CgHigOH 

o. 

.842 

—  5- 

213. 

and  also  Wroblew- 

Decyl  alcohol 
Dodecyl  alcohol 

Ci0H21OH 

+  7- 
24. 

•839 
.831 

+  7- 
24. 

I43-* 

ski  and  Olszewski, 
"  Monatshefte," 

Tetradecyl  alcohol 

C14H29OH 

38. 

.824 

38. 

167.* 

vol.  4,  p.  338. 

Hexadecyl  alcohol 

C16H33OH 

.818 

190.* 

Octadecyl  alcohol 

Ci8H37OH 

59- 

.813 

59- 

211.* 

(e)  Alcoholic  ethers  :  C^H2M+2O. 

Dimethyl  ether   .     .     . 

C2H60 

- 

- 

- 

-23.6 

Erlenmeyer,  Kreich- 

baumer. 

Diethyl  ether  .     . 
Dipropyl  ether    . 

C4H100 
C6H140 

4- 
o. 

Q-731 
•763 

— 

+  34-6 
90.7 

Regnault. 
Zander  and  others. 

Di-iso-propyl  ether 
Di-n-butyl  ether  . 

C6H140 
C8Hi80 

o. 

0. 

•743 
.784 

- 

69. 
141. 

Lieben,  Rossi,  and 
others. 

Di-sec-butyl  ether 

C8H180 

21. 

.756 

- 

121. 

Kessel. 

Di-iso-butyl      "            . 

C8H180 

15. 

.762 

— 

122. 

Reboul. 

Di-iso-amyl      " 
Di-sec-hexyl     " 

CioH22O 
Ci2H260 

O. 

•799 

- 

170.-!  7  5. 

2O3.-2O8. 

Wurtz. 
Erlenmeyer  and 
Wanklyn. 

Di-norm-octyl  "       .     . 

CioHwO 

17- 

.805 

- 

280.-282. 

Moslinger. 

(f)  Ethyl  ethers  :  CWH2W+2O. 

Ethyl-methyl  ether  .     . 
"     propyl      "       .     • 
"     iso-propyl  ether  . 
"     norm-butyl  ether 
"     iso-butyl  ether     . 
"     iso-amyl  ether 

C3H80 
C5H120 
C5H120 
C6Hi40 
C6H140 
C7H160 

20. 
o. 
o. 

18. 

o-739 

- 

II. 
63.-64- 
54- 
92. 
;8.-8o. 

112. 

Wurtz,  Williamson. 
Chancel,  Briihl. 
Markownikow. 
Lieben,  Rossi. 
Wurtz. 
Williamson  and 
others. 

"     norm-hexvl  ether 

C8H180 

- 

- 

- 

J34--I37- 

Lieben,  Janeczek. 

"     norm-heptyl  ether 
"     norm-octyl  ether 

C9H200 

1  6. 
17- 

.790 
•794 

- 

165. 
i82.-i84. 

Cross. 
Moslinger. 

*  Boiling-point  under  15  mm.  pressure. 

t  Liquid  at  — u.°  C.  and  180  atmospheres'  pressure  (Cailletet). 


SMITHSONIAN  TABLES. 


213 


TABLE  221 


COEFFICIENTS  OF  THERMAL    EXPANSION. 

Coefficients  of  Linear  Expansion  of  the  Chemical  Elements. 

In  the  heading  of  the  columns  T  is  the  temperature  or  range  of  temperature,  C  the  coefficient  of  linear  expansion, 
A  the  authority  for  C  M ihe  mean  coefficient  of  expansion  between  o°  and  100°  C.,  a  and  ft  the  coefficients  in  the 
equation  lt  —  lQ  (i  +  a/ +  /&»),  where  10  is  the  length  at  o°  C.  and  It  the  length  at  *°  C.,  ^2  is  the  authority  for  o, 
ft,  and  m. 


Substance. 

T 

c 

Xio* 

,, 

M 

Xio* 

Xio4 

13  o 

A, 

Aluminium      .     . 

40 
600 

0-2313 
•3150 

Fizeau  .     .     . 
Les  Chatelier. 

0.2220 

- 

(  Calvert,  John- 
(  son  and  Lowe. 

Antimony  : 

Parallel  to  cryst. 

axis  .... 

40 

.1692 

Fizeau. 

• 

Perp.  to  axis 
Mean   .... 

40 
40 

.1152 

"... 

.1056 

.0923 

.0132 

Matthieson. 

Arsenic  .... 

40 

•0559 

" 

Bismuth-: 

Parallel  to  axis 

40 

.1621 

« 

Perp.  to  axis 

40 

.1208 

« 

Mean    .... 

40 

.1346 

"... 

.1316 

.1167 

.0149 

Matthieson. 

Cadmium    .     .     . 

40 

.3069 

"... 

•3159 

.2693 

.0466 

M 

Carbon  : 

Diamond  .     .     . 

40 

.0118 

" 

Gas  carbon  .     . 

40 

.0540 

" 

Graphite  .     .     . 

40 

.0786 

u 

Anthracite    .     . 

40 

.2078 

" 

Cobalt    .... 

40 

.1236 

" 

Copper   .... 
Gold 

40 

.1678 

u 

.1666 

.1481 

.0185 
.OI  1  2 

Matthieson. 

M 

Indium    .... 

40 

.4170 

« 

.1470 

•J35 

Iron  : 

Soft      .... 

40 

.1210 

" 

Cast     .... 

40 

.I06l 

" 

Wrought  .     .     . 

—  i8to  100 

.II4O 

Andrews. 

Steel    .... 

40 

.1322 

Fizeau. 

"      annealed 

40 

.1095 

"... 

.I089 

.1038 

.0052 

Benoit. 

Lead  

40 

M 

.27OQ 

O?*7  1 

.OO74. 

Matthieson. 

Magnesium      .     . 

T-W 
40 

^§94 

« 

•*/  wy 

' 

:\J^J/  if 

Nickel     .... 

40 

.1279 

" 

Os'mium 

40 

.0657 

* 

Palladium    .     .     . 

40 

.1176 

"... 

.1104 

.ion 

.0093 

Matthieson. 

Phosphorus      .     . 

0-40 

1-2530 

Pisati  and  De 

Franchis. 

Platinum     .     .     . 

40 

.0899 

Fizeau  .     .     . 

.0886 

.0851 

•°°35 

Matthieson. 

Potassium   .     .     . 

0-50 

.8300 

Hagen. 

Rhodium     .     .     . 

40 

.0850 

Fizeau. 

Ruthenium  . 

40 

.0960 

" 

Selenium     .     .     . 

40 

.3680 

"... 

.6604 

- 

_ 

Spring. 

Silicon    .... 

40 

.0763 

u 

Silver      .... 

40 

.1921 

"... 

•1943 

.1809 

•0135 

Matthieson. 

Sulphur  : 

Cryst.  mean  .     . 

40 

.6413 

"... 

1.180 

_ 

_ 

Spring. 

Tellurium    .     .     . 

40 

•1675 

"... 

.3687 

_ 

_ 

1  Thallium     .     .     . 

40 

.3021 

" 

Tin 

AC\ 

« 

^; 

/* 

AT     4-*V»  tAf  *-\*t 

Q\J 

***  34 

•  -iZCJO 

•2033 

.2003 

iVlctLinicSOIl. 

Zinc    

4.O 

.2918 

M 

^n*7^ 

_ 

II 

.02  ^4 

N.  B.  —  The  above  table  has  been  with  a  few  exceptions  compiled  from  the  results  published  by  Fizeau,  "  Comptes 
Rendus,    vol.  68,  and  Matthieson,  "  Proc.  Roy.  Soc.,;'  vol.  15. 


SMITHSONIAN  TABLES. 


214 


TABLE  222. 


COEFFICIENT   OF   THERMAL    EXPANSION. 

Coefficient  of  Linear  Expansion  for  Miscellaneous  Substances. 

N.  B.  —  The  coefficient  of  cubical  expansion  may  be  taken  as  three  times  the  linear  coefficient.     T  is  the  temperature 
or  range  of  temperature,  C  the  coefficient  of  expansion,  and  A  the  authority. 


Substance. 

T 

CX  10* 

A 

Substance. 

T 

CXio< 

A 

Brass  : 

Cast      . 

0-100° 

0.1875 

I 

Platinum-silver  : 

Wire    . 

" 

0.1930 

I 

lPt+2Ag 

0-100° 

0.1523 

4 

.... 

" 

.1783-.  1930' 

2 

Porcelain 

20-790 

0.0413 

16 

7i.5Cu+27.7Zn+ 

"          Bayeux    . 

IOOO-I4OO 

0.0553 

17 

0.3811+0.  5?b 

40 

0.1859 

3 

Quartz  : 

7iCu+29Zn 

O-IOO 

0.1906 

4 

Parallel  to  axis     . 

0-80 

0.0797 

6 

Bronze  : 

Perpend,  to  axis  . 

" 

0.1337 

6 

3Cu+iSn     . 

166-100 

0.1844 

5 

Speculum  metal 

O-IOO 

0.1933 

i 

"         " 

16.6-350 

0.2116 

5 

Topaz  : 

S6.3Cu+9.7Sn+ 
4Zn 

16.6-957 
40 

0.1737 

0.1782 

5 
3 

Parallel  to  lesser 
horizontal  axis 
Parallel  to  greater 

M 

0.0832 

8 

97.6Cu+2.2Sn+ 
0.2?,  hard 

0-80 

0.1713 

6 

horizontal  axis 
Parallel    to   verti- 

0.0836 

8 

u     «  u  u       soft 

" 

0.1708 

6 

cal  axis 

" 

0.0472 

8 

Caoutchouc 

_ 

.657-.686 

2 

Tourmaline  : 

16.7-25.3 

0.770 

7 

Parallel  to   longi- 

Ebonite   . 

25-3-35-4 

0.842 

tudinal  axis 

" 

0.0937 

8 

Fluor  spar  :  CaF-2    . 
German  silver  . 

O-IOO 

0.1950 
0.1836 

8 

Parallel    to    hori- 
zontal axis 

M 

0.0773 

8 

Gold-platinum  : 
2Au+iPt 
Gold-copper  : 

M 

0-1523 

4 

Type  metal 
Vulcanite 
Wedgwood  ware 

16.6-254 
0-18 

O-IOO 

0.1952 

0.6360 

,3 

5 

2Au+iCu 
Glass  : 

u 

0-155* 

4 

Wood: 
Parallel  to  fibre  : 

Tube    .        . 

« 

0.0833 

i 

Ash  . 

u 

0.0951 

19 

« 

0.0828 

9 

Beech 

2-34 

0.0257 

20 

Plate    .' 

u 

0.0891 

10 

Chestnut  . 

0.0649 

20 

Crown  (mean) 

" 

0.0897 

10 

Elm  . 

" 

0.0565 

20 

50-60 

0.0954 

ii 

Mahogany 

0.0361 

20 

Flint     . 

«    . 

0.0788 

ii 

Maple       . 

u 

0.0638 

20 

Jena  thermometer 
(normal) 

O-IOO 

0.08  1 

0.058 

12 
12 

Oak  . 
Pine  . 
Walnut     . 

tl 

0.0492 
0.0541 

0.0658 

20 
20 
20 

Gutta  percha  . 
Ice  . 

20 

-20  to  -i 

1-983 

o-375 

14 

Across  the  fibre  : 
Beech 

« 

0.614 

20 

Iceland  spar  : 

Chestnut  . 

M 

0.325 

2O 

Parallel  to  axis     . 
Perpendicular    to 
axis 

0-80 

0.2631 
0.0544 

6 
6 

Elm  . 
Mahogany 
Maple        . 

u 

0.443 
0.404 

0.484 

20 
20 
20 

Lead-tin  (solder) 
2Pb+iSn 
Paraffin    .     •   .   .     . 

Platinum-iridium 
loPt+iIr 

0-100 
0-16 

16-38 
38-49 

40 

0.2508 
1.0662 
1.3030 
4-7707 

0.0884 

i 
15 

1C 

Oak  . 
Pine  .        ... 
Walnut     . 
Wax:  White   . 

M 

If 

IO-26 
26-31 
3^43 

43-57 

0.544 
0.341 
0.484 
2.300 
3.120 
4.860 
15.227 

20 
20 
20 
21 
21 
21 
21 

1 

AUTHORITIES. 

T  Smeaton           6  Benoit                            iiPulfrich.        16  Braun.                           21  Kopp. 
*S£?          7  Kohlrausch.                   12  Schott.          17  Neville  and  Troost. 
\  Fi/eau.             8  Pfaff.                              13  Russner.       18  Mayer 
4Matthieson.     9  Deluc.                             14  Brunner        19  Glatzel. 
5  Daniell        10  Lavoisier  and  Laplace.     15  Rodvvell.       20  Vill 

SMITHSONIAN   TABLES. 


215 


TABLE  223. 

COEFFICIENTS    OF    THERMAL    EXPANSION. 

Coefficients  of  Cubical  Expansion  of  seme  Crystalline  and  other  Solids.* 

T rr  temperature  or  range  of  temperature,  C=  coefficient  of  cubical  expansion,  A  =  authority. 


Substance. 

T 

CX  io» 

A 

Antimony   .... 

O-IOO 

0.3167 

Matthieson. 

Beryl  .        .  '      . 

O-IOO 

0.0105 

Pfaff. 

Bismuth      .... 

- 

0.4000 

Kopp. 

Diamond    .... 

40 

0.0354 

Fizeau. 

Emerald      .... 

40 

0.0168 

" 

Fluor  spar  .... 

14-47 

0.6235 

Kopp. 

Garnet        .... 

O-IOO 

0.2543 

Pfaff. 

Glass,  white  tube 

O-IOO 

0.2648 

Regnault. 

"       green  tube 

c-ioo 

0.2299 

a 

"       Swedish  tube  . 

O-IOO      . 

0.2363 

« 

"       hard  French  tube    . 

O-ICO 

0.2142 

H 

"       crystal  tube 

O-IOO 

0.2IOI 

« 

"       common  tube  . 

O-I 

0.2579 

« 

"       Jena 

O-IOO 

0-2533 

Reichsanstalt. 

Ice      

—  20  tO  —  I 

1.1250 

B  runner. 

Iceland  spar 

50-60 

0.1447 

Pulfrich. 

Idocrase      .... 

O-IOO 

0.2700 

Pfaff. 

Iron    

O-IOO 

0-355° 

Dulong  and  Petit. 

« 

O—  7OO 

r\  A  A  i  r\ 

«               u             « 

Magnetite,  FegC^ 

\J     jt-'w 

O-IOO 

U.^-f  J  U 

0.2862 

Pfaff. 

Manganic  oxide,  Mn2O3     . 

O-IOO 

0.522 

Playfair  and  Joule. 

Orthoclase  (adularia) 

O-IOO 

0.1794 

Pfaff. 

Porcelain 

O-IOO 

0.1080 

Deville  and  Troost. 

Quartz        ... 

50-60 

°-353° 

Pulfrich. 

Rock  salt    .        .        . 

50-60 

1.  2120 

« 

Spinel  ruby 

40 

0.1787 

Fizeau. 

Sulphur,  rhombic 

O-IOO 

2.2373 

Kopp. 

Topaz         .... 

O-IOO 

0.2137 

Pfaff. 

Tourmaline 

O-IOO 

0.2181 

« 

Zincite,  ZnO 

40 

0.0279 

Fizeau. 

Zircon         .... 

O-IOO 

0.2835 

Pfaff. 

SMITHSONIAN  TABLES. 


'   see   Clarke's   "Constants   of   Nature, 


216 


TABLE  224. 
COEFFICIENTS  OF  THERMAL  EXPANSION. 

Coefficients  of  Cubical  Expansion  of  Liquids. 

This  table  contains  the  coefficients  of  expansion  of  some  liquids  and  solutions  of  salts.  When  not  otherwise  stated 
atmospheric  pressure  is  to  be  understood.  T  gives  the  temperature  range,  C  the  mean  coefficient  of  expansion 
for  range  T  in  degrees  C.,  and  Al  the  authority  for  C.  a,  /3,  and  y  are  the  coefficients  in  the  volume  equation 
vt  =.  v0  (i  +  o/  -f-  ftp  -f  Y/3),  and  m  the  mean  coefficient  for  range  ou-ioo°  C.,  and  A9  is  the  authority  for  these. 


Liquid. 

T 

C 

X  looo 

- 

m 

X  100 

a  X  looo 

/3Xio« 

y  X  io8 

., 

Acetic  acid      .... 

i6°-io7° 

_     . 

_ 

T433 

1.0630 

0.1264 

1.0876 

3 

Acetone                         • 

O—  C4 

1616 

T    I^/IO 

I.SOOO 

O.8708 

7 

Alcohol  : 

'•'j'f 

j.uwyj 

*****/  v^j 

J 

Amyl            .... 

—  I  C  tO  4-8o 

_ 

_ 

_ 

0.8900 

0.6573 

1.1846 

4 

Ethyl,  sp.  gr.  .8095   . 
"    50  %  by  volume 

M.  ^      LW         pWW 
0-80 

o-39 

- 

- 

"-•»— 

01-0414 
0.7450 

0-783*? 
1.850 

1.7168 
0.730 

I 

"    30%    "     " 

18-39 

- 

- 

- 

0.2928 

I7.QOO 

11.87 

6 

"    500  atmo.  press. 

0-40 

.866 

i 

— 

— 

— 

— 

— 

"    3000   "         " 

0-40 

•524 

i 

— 

— 

— 

— 

— 

Methyl                  .     . 

—  38  to  -{-70 

t_ 

1433 

1.1856 

1.5649 

0.91  1  1 

4 

Benzene                          • 

11-81 

1385 

1.176^ 

I.277C 

0.8065 

5 

Bromine      

—  7  to  -{-60 

- 

- 

1168 

/      O 

1.0382 

/  /  J 

1.7114 

0-5447 

4 

Calcium  chloride  : 

CaCl2,  5.8  %  solution 
CaCl2,  40.9  %      "      . 
Carbon  disulphide   .     . 

18-25 
17-24 
—34  to  +60 

- 

- 

.0506 
0510 
.1468 

0.0788 
0.4238 
1.1398 

4.2742 
0.8571 
1.3706 

1.9122 

7 
7 
4 

500  atmos.  pressure  . 

0-50 

.940 

i 

— 

— 

•" 

"• 

" 

3000      " 

0-50 

.581 

i 

— 

— 

— 

~ 

"* 

Chloroform     .... 

0-63 

- 

•1399 

1.1071 

4.6647 

1-7433 

4 

Tether 

—  ic  to  +78 

_ 

_ 

.2150 

1.5132 

2-3592 

4.0051 

4 

Glycerine    

*  j   *"v      1    O 

- 

- 

•0534 

0.4853 

0.4895 

8 

Hydrochloric  acid  : 

0-30 

_ 

_ 

.0489 

0.4460 

0.430 

_ 

9 

HC1  +  5oH20      .    . 
>  Mercury      
.Olive  oil      

0-30 
24-299 

- 

- 

•0933 
^0742 

0.0625 
0.1818 
0.6821 

8.710 
0.000175 
1.1405 

0.003512 
—-539 

9 

IO 

ii 

Potassium  chloride  : 

KC1,  2.5  %  solution  . 

- 

- 

- 

.0572 

— 

— 

"" 

7 

KC1,  24-3%      " 

- 

- 

— 

.0477 

~ 

~ 

7 

Potassium  nitrate  : 

KN03,  5-3  %  sol'n 

- 

- 

- 

•0539 

— 

"* 

12 

KN03,  21.9%      " 
Phenol,  C6H6O   .     .     . 

36-157 

_ 

_ 

•0577 
.0899 

0.8340 

0.1073 

0.4446 

1  2 

Petroleum  
Sp.  gr.  0.8467  .     .     . 

7-38 
24-120 

.992 

2 

.1039 

0.8994 

1.396 

- 

14 

Sodium  chloride  : 
NaCl,  i.  6%  solution. 

_ 

_ 

- 

.1067 

0.0213 

10.462 

- 

9 

Sodium  sulphate  : 
Na2SO4,  24  %  sol'n  . 

10-40 

- 

- 

.0611 

0-3599 

2.516 

- 

9 

Sodium  nitrate  : 
NaNO3,  36.2  %  sol'n  . 

20-78 

_ 

- 

.0627 

0.5408 

1-075 

- 

12 

Sulphuric  acid  : 
H2S04     .... 
H2SO4  +  5oH2O 
Turpentine      .     •     • 
Water 

0-30 
0-30 
—9  to  +106 

0-200 

- 

- 

.0489 
.0799 

0.5758 
0.2835 
0.9003 
—.0658 

0.864 
5.160 
1-959 
8.507 

-6.769 

9 
9 

5 
15 

AUTHORITIES. 

A                           A  Pierre                    7  Decker.              10  Broch.             13  Pinette. 
i  Amagat.                                                /   EmQ                  TI  gpring.            14  Frankenheim. 

3  Zander.                6  Recknagel.            9  Marignac.          12  Nicol. 

SMITHSONIAN  TABLES. 


217 


TABLE  225. 


COEFFICIENTS   OF  THERMAL   EXPANSION. 


Coefficients  of  Expansion  of  Gases. 

The  numbers  obtained  by  direct  experiment  on  tlie  change  of  volume  at  constant  pressure,  EP,  are  separated  in  the 
table  from  those  obtained  from  the  change  of  pressure  at  constant  volume,  Ev.  The  two  parts  of  the  table  are 
headed  "  Coefficient  at  constant  pressure  ''  and  "  Coefficient  at  constant  volume,"  respectively.  Ordinary  changes 
of  atmospheric  pressure  produce  very  little  change  in  the  coefficient  of  expansion,  and  hence  entries  in  the  pressure 
column  of  i  atm.  have  been  made  for  all  pressures  near  to  76  centimetres  of  mercury.  The  other  numbers  in  the 
pressure  columns  are  centimetres  of  mercury  at  o°  C.  and  approx.  45°  latitude,  unless  otherwise  marked. 

Thomson  has  given  (vide  Encyc.  Brit.  art.  "Heat")  the  following  equations  for  the  calculation  of  the  expan- 
sion, .£",  between  o°  and  100°  C.  of  the  gases  named.  Expansion  is  to  be  understood  as  change  of  volume  under 
constant  pressure. 

Hydrogen    .     .     .     E  —  .  3662  (i  —.00049  -°) 

*  7/0  " 


Common  air 
Oxygen  .  . 
Nitrogen  . 


E  =  .3662  (i  -f  .0026  — °\ 
^  =  .3662(1  + .0032  -°) 
£  =  .3662  ( i  -f  .0031  ^\ 

Carbon  dioxide    .     E  —  .3662  (  i  -f-  .0164  — °  ) 
V  vo/ 

where  F0/»0  is  the  ratio  of  the  actual  density  of  the  gas  at  o°  C.  to  the  density  it  would  have  at  o°  C.  and  one 
atmosphere  of  pressure.  The  same  experiments  (Thomson  &  Joule,  Trans.  Roy.  Soc.  1860), — which,  together 
with  Regnault's  data,  led  to  these  equations,  —  give  for  the  absolute  temperature  of  melting  ice  2.731  times  the 
temperature  interval  between  the  melting-point  of  ice  and  the  boiling-point  of  water  under  normal  atmospheric 
pressure. 


Coefficient  at  constant  volume. 

Coefficient  at  constant  pressure.t 

Substance. 

Pressure. 

Ev 
Xioo 

"5  >, 

Substance. 

Pressure. 

Xioo. 

o 

Air       .        . 

0.6 

•3765 

Air    . 

76. 

0.3671 

3 

" 

1.6 

•37°3 

" 

257- 

0-3695 

3 

"         .         . 

7-6 

.3665 

Hydrogen  . 

76. 

s-s 

0.36613 

3 

" 

IO.O 

•3663 

"... 

254- 

0.36616 

3 

M 

26.0 

.3660 

Carbon  dioxide 

76. 

0.3710 

3 

" 

37-6 

.3662 

"             " 

252. 

0.3845 

"              .              • 

75-o 

•3665 

"            "     o°-64° 

17.1  atm. 

0.5136 

6 

" 

76-83 

.3670 

2* 

"  64°-ioo°j  17.1     " 

0.4747 

6 

" 

11-15 

.3648 

3 

"     o°-7.5° 

24.81  « 

0.7000 

6 

" 

17-24 

.3651 

3 

"     o°-64° 

24.81  " 

0.6204 

6 

(i 

37-51 

•3658 

3 

"    64°-!  00° 

24.81  « 

0-5435 

6 

" 

76 

.3665 

3 

"    o°-7.50 

34-49  " 

1.0970 

6 

" 

200 

•3690 

3 

"    o°-64° 

34-49  " 

0.8450 

6 

. 

2OOO 

.3887 

3 

"      0°-IOO° 

34-49  " 

0-6574 

6 

" 

1  0000 

4100 

3 

Carbon  monoxide 

76. 

0.3669 

3 

"              .              .              .              . 

76 

.3669 

3* 

Nitrous  oxide    . 

76. 

0.3719 

3 

II 

Carbon  dioxide   . 

76 

i  atm. 

.3671 
.3670 
.3706 

4 
5* 

5 

Sulphur  dioxide 
Water  vapor,  o°-ng° 

76. 
98. 
atm. 

0.3903 
0.3980 
0.4187 

3 

3 

7 

" 

i     " 

.3726 

i 

"           "      o°—  141° 

" 

0.4189 

7 

'            " 

76-104 

.3686 

3 

"        0°-l62° 

u 

0.4071 

7 

"         .    ''    • 

174-234 

•3752 

3 

"        0°-200° 

" 

0-3938 

7 

U                         if 

"    0^-64°  '. 

793 
16.4  atm. 

.4252 

•4754 

I 

"      o°-247° 

0-3799 

7 

'"              "    64°—  1  00° 

16.4     " 

.4607 

6 

"      o°-64°  . 
"    64c-ioo° 

25.87  « 
25.87  « 

.5728 
.5406 

6 
6 

AUTHORITIES. 

"      o°-64°  . 

33-53    ' 

•6973 

6 

i  Melander.                  5  Jolly. 

"    64°-ioo° 
Carbon  monoxide 

33-53    ' 
i        ' 

•6334 
•3667 

6 
3 

2  Magnus.                     6  Andrews. 
3  Regnault.                  7  Hirn. 

Hydrogen    . 

i        ' 

-3669 

3 

4  Rowland. 

Nitrogen 

« 

^3668 

5 
3 

Nitrous  oxide 

1 

.3676 

3 

.                 . 

' 

.3707 

C 

Oxygen 

< 

jt   i 
.3674 

J 

5 

Sulphur  dioxide,  SO2  . 

•3845 

5 

Corrected  by  Mendelejeff  to  45°  latitude  and  absolute  expansion  of  mercury. 
correction  on  Regnault,  using  Wiillner's  value  of  the  expansion  of  mercury. 

T  i  he  series  of  results  at  different  pressures  are  given  because  of  their  interest. 
too  low.    (See  preceding  footnote.) 

SMITHSONIAN  TABLES. 

218 


Rowland  gets  almost  the  same 
The  absolute  values  are  a  little 


TABLE  226. 
DYNAMICAL    EQUIVALENT   OF   THE  THERMAL    UNIT. 

Rowland  in  his  paper  quoted  in  Table  227  has  given  an  elaborate  discussion  of  Joule's  determinations  and  the  cor- 
sctions  required  to  reduce  them  to  temperatures  as  measured  by  the  air  thermometer.     The  following  table  con- 
tarns  the  results  obtained,  together  with  the  corresponding  results  obtained  in  Rowland's  own  experiments.    The 
variation  for  change  of  temperature  in  Rowland's  result  is  due  to  the  variation  with  temperature  of  the  specific  heat 
of  water. 


Date. 


1847 
1850 
1850 
1850 
1850 
1850 
1867 
1878 
1878 
1878 
1878 
1878 


Method  of  experiment. 


Friction  of  water    . 
«         «       <« 

"         "   mercury 
»<         «<         « 

"        "  iron 
«        (i      «( 

Electric  heating .     . 
Friction  of  water    . 


Temp, 
of 


1$ 

14 

9 

9 

9 

9 

18.6 
14.7 
12.7 
15-5 
14-5 
17-3 


Joule's 
value. 


781.5 

772.7 
772.8 

775-4 
776.0 

773-9 

772.7 
774.6 

773-1 
767.0 
774.0 


Joule's  value  reduced 

to  air  thermometer 

and  latitude  of 

Baltimore. 


Eng.  units.  Met.  units 


787.0 
778.0 
779.2 
781.4 
782.2 
780.2 

776.1 

778.5 
776.4 

770-5 
777.0 


442-8 
426.8 

427.5 
428.7 
429.1 
428.0 
428.0 
425.8 
427.1 
426.0 
422.7 
426.3 


Row- 
land's 
value. 


427.4 
427.7 
428.8 
428.8 
428.8 
428.8 
426.7 
427-6 
428.0 
427.3 
427-5 
426.9 


J-R. 


+  15-4 
—0.9 

—i-3 
—  o.i 

+0.3 
—0.8 


—0.9 

—  1-3 

-4.8 
-0.6 


From  the  above  values  and  weights  Rowland  concludes  as  the  most  probable  value 
from  Joule's  experiments,  at  the  temperature  14.6°  C.  and  the  latitude  of  Baltimore,  426.75, 
and  from  his  own  experiments  427.52. 

The  mean  of  these  results  is  427.13  in  metric  units,  or  778.6  in  British  units.  Correct- 
ing back  for  latitude,  and  to  mercury  thermometer,  this  gives  about  774.5  for  the  latitude 
of  Manchester,  instead  of  772,  as  has  been  commonly  used. 

An  elaborate  determination  recently  made  by  Griffith  and  referred  to  in  Table  227  gives 
a  value  about  one  tenth  of  one  per  cent  higher  than  Rowland's.  Probably  when  a  mer- 
cury thermometer  is  involved  in  the  measurements  we  may  take  776  as  the  nearest  whole 
number  in  foot-pounds  and  British  thermal  units  for  the  latitude  of  Manchester,  and  777 
for  that  of  Baltimore.  The  corresponding  values  in  the  metric  system  will  be  425.8  and 
426.3,  or  in  round  numbers  426  for  both  latitudes. 

The  following  quantities  should  be  added  to  the  equivalent  of  Baltimore  to  give  the 
equivalent  at  the  latitude  named  :  — 

Latitude      ....   0°     10°     20°      30°    40°      50°        60°        70°        80°        90° 

Kilogramme-metres  0.89    0.82    0.63    0.34    0.08  —0.41    —0.77    — 1.06    —1.26     —1.33 
Foot-pounds  .     .    .   1.62    1.50    1.15    0.62    0.15  —0.75    —1.41    — 1-93    —  2-3°     —2-43 


SMITHSONIAN  TABLES. 


219 


TABLE  227, 


MECHANICAL  EQUIVALENT  OF  HEAT. 

The  following  historical  table  of  the  principal  experimental  determinations  of  the  mechanical  equivalent  of  the  unit  of 
heat  has  been,  with  the  exception  of  the  few  determinations  bearing  dates  later  than  1879,  taken  from  Rowland.* 
The  different  determinations  are  divided  into  four  groups,  according  to  the  method  used.  Calculations  based  on 
the  constants  of  gases  and  vapors  as  determined  by  others  are  not  included  in  this  table. 


Method. 

Observer. 

Date. 

Result. 

Joule  1 

1841; 

8 

Expansion       "    " 

Joule  1 

i>jHO 
1845 

437^8 

Experiments  on  steam  engine   . 

Him2 

1857 

413.0 

"              "       "            "... 

Him2 

1860-1 

420-432 

( 

443-6 

Expansion  and  contraction  of  metals 

Edlund  8 

1865    ] 

430.1 

( 

428.3 

«            « 

Haga* 

1881    | 

437-8 
428.1 

Measurement  of  the   specific  volume  of 

vapor      

Perot  5 

1886 

424-3 

Boring  of  cannon        

Rumford  6 

1798 

940  ft.-lbs. 

Friction  of  water  in  tubes 

Joule  7 

1843 

424.6 

"      "      "  calorimeter 

Joule  i 

1845 

488.3 

«      (i      «            u, 

Joule8 

1847 

428.9 

«        u        u               "... 

Joule  9 

1850 

423.9 

"  mercury  in       "... 

Joule  » 

1850 

424.7 

"  plates  of  iron 

Joule  • 

1850 

425.2 

"  metals      

Him2 

1857 

371.6 

in  mercury  calorimeter  . 

Favre  10 

1858 

413.2 

Boring     "       "            '.'.'.'.'. 

Him2 
Him2 

1858 
1858 

400-450 

Water  in  balance  afrottement   . 

Him2 

1860-1 

432.0 

Flow  of  liquids  under  strong  pressure 
Crushing  of  lead        

Him  2 
Jlirn2 

1860-1 
1860-1 

T»J 

432.0 
425.0 

Friction  of  metals      .... 

Puluj  n 

1876 

426.6 

Friction  of  water  in  calorimeter 

«        <«       «      «          K 

Joule  12 
Rowland  18 

1878 
1879 

423.9 
426.3 

"        "  metals                               '.        \ 

Sahulka  " 

1890 

.              427.S 

Heating  by  magneto-electric  currents 

Joule  7 

1843 

460.0 

Heat  generated  in   a  disc  between   the 

f 

435-2 

poles  of  a  magnet  

Violle  15 

1870  j 

434-9 
435-8 

Flow  of  mercury  under  pressure 
Heat  developed  in  wire  of  known  abso-  j 
lute  resistance         ) 

Bartoli  16 
Quintus  Icilius,17 
also  Weber 

1880 
|    1857 

437-4 
428.4 

399-7 

Heat  developed  Jn  wire  of  known  abso-  ( 

Lenz 

i               ( 

396-4 

lute  resistance         \ 

Weber 

j    I859   j 

4.78.2 

Heat  developed  in  wire  of  known  abso- 

*T/ ^••6r 

lute  resistance         .... 

Joule  18 

1867 

429-5 

Heat  developed  in  wire  of  known  abso- 

lute resistance         
Heat  developed  in  wire  of  known  abso- 
lute resistance         .... 

H.  F.  Weber  19 
Webster  *> 

1877 
1885   ] 

428.15 

4  14X10*  ergs  per 
gramme  degree. 

Heat  developed  in  wire  of  known  abso- 

lute resistance 

Dieterici  21 

1888 

424.36 

REFERENCES. 

See  opposite  page. 

SMITHSONIAN  TABLES, 


*  "  Proc.  Am.  Acad.  Arts  and  Sci."  vol.  15. 
220 


TABLE  227, 


MECHANICAL  EQUIVALENT  OF  HEAT. 


Method. 

Observer. 

Date. 

Result. 

Diminishing    the    heat   contained   in   a  battery 

when  the  current  produces  work 

Joule  7 

1843 

499.0 

Diminishing    the   heat   contained   in   a  battery 

when  the  current  produces  work 

Favre  » 

1858 

443-° 

Heat  due  to  electrical  current,  electro-chemical 

Weber,       ] 

equivalent  of  water  =  .009379,  absolute  resist- 
ance, electro-motive  force  of  Uaniell  cell,  heat 

Boscha, 
Favre, 

l857 

432.1 

developed   by   action  of  zinc  on  sulphate  of 

and 

copper        

Silbermann 

Heat  developed  in  Daniell  cell     .... 
Electromotive  force  of  Daniell  cell 

j         Joule         I 
\       Boscha23    J 

1859 

4i9o 

Combination  of  electrical  heating  and  mechan- 

ical action  by  stirring  water      .... 

Griffiths  2* 

1893 

428.0 

REFERENCES. 

1  Joule,  "  Phil.  Mag."  (3)  vol.  26. 

2  Him,  "  Theorie  Mec.  de  la  Chaleur,"  ser.  i,  3tne  ed. 

3  Edlund,  "  Pogg.  Ann."  vol.  114. 

4  Haga,  "  Wied.  Ann."  vol.  15. 

5  Perot,  "  Compt.  Rend."  vol.  102. 

6  Rumford,  "  Phil.  Trans.  Roy.  Soc."  1798 ;  Favre,  "  Compt.  Rend."  1858. 

7  Joule,  "  Phil.  Mag."  (3)  vol.  23. 

8  Joule,        "         "         "      "    27. 

9  Joule,        "        "        "      "    31- 

10  Favre,  "  Compt.  Rend."  1858  ;  "  Phil.  Mag."  (4)  vol.  15. 

11  Puluj,  "  Pogg.  Ann."  vol.  157. 

12  Joule,  "Proc.  Roy.  Soc."  vol.  27. 

13  Rowland,  "  Proc.  Am.  Acad.  Arts  &  Sci.'^  vols.  15  &  16. 

14  Sahulka,  "  Wied.  Ann."  vol.  41. 

15  Violle,  "Ann.  de  Chim."  (4)  vol.  22. 

16  Bartoli,  "  Mem.  Ace.  Lincei,"  (3)  vol.  8. 

17  Quintus  Icilius,  "  Pogg.  Ann."  vol.  101. 

18  Joule,  "  Rep.  Com.  on  Elec.  Stand.,"  "  B.  A.  Proc."  1867. 

19  H.  F.  Weber,  "  Phil.  Mag."  (5)  vol.  5. 

20  Webster,  "  Proc.  Am.  Acad.  Arts  &  Sci."  vol.  20. 

21  Dieterici,  "  Wied.  Ann."  vol.  33. 

22  Favre,  "  Compt.  Rend."  vol.  47. 

23  Boscha,  "  Pogg.  Ann."  vol.  108. 

24  Griffiths,  "  Phil.  Trans.  Roy.  Soc."  1893. 


SMITHSONIAN  TABLES. 


221 


TABLES  228,  229. 

SPECIFIC   HEAT. 

Specific  Heat  of  Water. 

The  specific  heat  of  water  is  a  matter  of  considerable  importance  in  many  physical  measure- 
ments, and  it  has  been  the  subject  of  a  number  of  experimental  investigations,  which  unfortu- 
nately have  led  to  very  discordant  results.  Regnault's  measurements,  published  in  1847,*  show 
an  increase  of  specific  heat  with  rise  of  temperature.  His  results  are  approximately  expressed 
by  the  equation 

c  =  i  -J-  .0004  t  -f-  0000009  /2, 

which  makes  the  specific  heat  nearly  constant  within  the  atmospheric  range.  A  different  equa- 
tion was  found  from  Regnault's  results  by  Boscha,  who  thought  the  temperatures  required  cor- 
rection to  the  air-thermometer.  Regnault,  however,  pointed  out  that  the  results  had  already 
been  corrected.  Jamin  and  Amaury  t  found,  for  a  range  from  9°  to  76°  C.,  the  equation 

C  =  I  -f  .001  1  /  +  .0000012  f8, 

which  nearly  all  the  evidence  available  shows  to  be  very  much  too  rapid  a  change.  Wullner 
gives,  for  some  experiments  of  Miinchhausen,!  the  equation 

f=I-\-  .000301  02  / 

in  vol.  i,  changed  to 

c=  i  -f  .000425  1 

in  vol.  10,  for  a  range  of  temperature  from  17°  to  64°.  In  1879,  -experiments  are  recorded  by 
Stamo,§  by  Henrichsen,||  and  by  BaumgartenJ  all  of  them  giving  large  variation  with  temper- 
ature. 

In  1879,  Rowland  inferred  from  his  experiments  on  the  mechanical  equivalent  of  heat  that  the 
specific  heat  of  water  really  passes  through  a  minimum  at  about  30°,  and  he  attempted  to  verify 
this  by  direct  experiment.  The  results  obtained  by  direct  experiments  were  not  by  any  means 
so  satisfactory  as  those  obtained  from  the  friction  experiment  ;  but  they  also  indicated  that  the 
specific  heat  passed  through  a  minimum,  —  but,  in  this  case,  at  about  20°  C.  Further,  direct 
experiments  were  made  in  1883,  in  Rowland's  laboratory,  by  Liebig,  using  the  same  calorimetric 
apparatus  ;  and  these  experiments  also  show  a  minimum  at  about  20°  C.1[  Since  the  publica- 
tion of  Rowland's  paper  a  number  of  new  determinations  have  been  made.  Gerosa  gave,  in 
1881,  a  series  of  equations  which  show  a  maximum  at  4°.4,  then  a  minimum  a  little  above  5°  and 
afterwards  a  rise  to  24°!  Neesen  **  found  a  minimum  near  30°,  but  got  rather  less  variation  than 
Rowland.  Rapp,tt  taking  the  mean  specific  heat  between  o°  and  100°  as  unity,  gives  the  equa- 
tion 

c=  1.039925  —  .007068  1-\-  .0002  1  2  55/2  —  .00000  1  584  /*, 

which  gives  a  minimum  between  20°  and  30°  and  a  maximum  about  70°.  VoltenJJ  gives  an 
equation  which  is  even  more  extraordinary  with  regard  to  coefficients  than  the  last,  namely, 

r=i  —  .0014625512  /+  .0000237981/2  —  .000000  1  07  1  6  /3, 

which  puts  the  minimum  between  40°  and  50°,  and  gives  a  maximum  at  100°;  which  maximum 
is,  however,  less  than  unity.  Dieterici,  in  his  paper  on  the  mechanical  equivalent  of  heat,  dis- 
cusses this  subject  ;  but  his  own  results  being  in  close  agreement  with  Rowland's,  his  table  prac- 
tically only  extends  Rowland's  results  through  a  greater  range  of  temperature,  assuming  straight- 
line  variation  to  the  two  sides  of  the  minimum.  Bartoli  and  Stracciati  §§  found  a  minimum  at 
about  30°;  while  Johanson  in  the  same  year  gives  a  minimum  at  about  4°  and  then  a  rise  about 
12  times  as  rapid  as  that  of  Regnault.  Griffiths  ||!|  finds  the  equation 

c  =  i  —  .0002666  (t  —  15) 

to  satisfy  his  experiments  through  the  range  from  15°  to  26°.  This  agrees  fairly  well  with  Row- 
land through  the  same  range,  and  indicates  that  the  minimum  is  at  a  temperature  higher  than 

The  following  table  gives  the  results  of  Rowland,  Bartoli  and  Stracciati,  and  Griffiths.  The 
column  headed  '«  Rowland  "  has  been  calculated  from  Rowland's  values  of  the  mechanical  equiv- 
alent of  heat  at  different  temperatures,  on  the  assumption  that  the  specific  heat  at  15°  is  equal  to 
unity. 


'  M£m.  de  PAcad."  vol.  21.  t  "  Compt.  Rend."  vol.  70,  1870. 

'  Wied.  Ann."  vols.  i  and  10.  §  "  Wied.  Beib."  voi.  3. 

* 


'Wied.  Ann.*'  vol.  8. 
1  Rowland,  "  Proc.  Am.  Acad."  vol.  15,  and  Liebig,  "Am.  Jour,  of  Sci."  vol.  26. 
'Wied.  Ann."  vol.  18,  1883. 

S    1 £'.ss;  Z£r£h,',"    ,  «  "  Wied.  Ann."  vol.  21,  1884. 

§§    'Wied.  Be»b."  vol.  15,  1891.  ||||  "Phil.  Trans."  1893. 

SMITHSONIAN  TABLES. 

222 


SPECIFIC   HEAT. 


TABLES  228-  229. 


TABLE  228. -Specific  Heat  of  Water. 


Temp. 

Rowland. 

Bartoli 
and 
Stracciati. 

Griffiths. 

Temp. 

Rowland. 

Bartoli 
and 

Stracciati. 

Griffiths. 

Dieterici. 

Temp. 
C. 

Specific 
heat. 

0° 

3 

4 

I 

1.0075* 
1.0070* 
1.0065* 
1.0060* 

1.0055* 

1.0050 

1.0045 

1.0040 

1.0034 

1.0066 
1.  0060 
1.0054 
1.0049 
1.0043 
1  .0038 
1.0033 
1.0028 
1.0023 

_ 

2O 
21 

22 

23 

24 

27 

0.9984 
0.9980 
0.9976 
0.9973 
0.9971 
0.9968 
0.9967 
0.9965 
0.9964 

0.9995 
0.9995 
0.9995 
0.9996 
0.9996 
0.9998 
I.OOOI 
1.0003 
1.  0006 

0.9989 
0.9987 
0.9984 
0.9981 
0.9979 
0.9976 
0.9973 
0.9971 
0.9967 

0° 
IO 

20 

3° 
40 

fi 
g 

I.OOOO 

0.9943 
0.9893 

0.9872 

0-9934 
0.9995 
1.0057 

I.OI2O 
I.OI82 

9 

1.0029 

I.OOI9 

— 

28 

0.9963 

I.OOIO 

9° 

1.0244      ! 

10 

1.0024 

I.OOI5 

- 

29 

0.9962 

1.0014 

_ 

IOO 

1  .0306      , 

ii 

1.0019 

I.OOII 

— 

30 

0.9962 

1.0019 

_ 

_ 

12 

1.0014 

1.0008 

- 

31 

0.9963 

1  .0024 

- 

_ 

_ 

*3 

1.0009 

1.0005 

— 

32 

0.9963 

— 

— 

_ 

_ 

14 

1.0005 

1  .0002 

— 

33 

0.9964 

— 

_ 

_ 

_ 

15 

I.OOOO 

I.OOOO 

I.OOOO 

34 

0.9965 

_ 

_ 

_ 

1  6 

0.9996 

0.9998 

0.9997 

35 

0.9966 

_ 

_ 

_ 

_ 

17 

0.9991 

0.9997 

0.9995 

36 

0.9967 

_ 

_ 

_ 

_ 

18 

0.9987 

0.9996 

0.9992 

TABLE  229. -Specific  Heat  of  Air. 

The  ratio  of  the  specific  heat  at  constant  pressure  to  the  specific  heat  at  constant  volume  has  been  the  subject  of  much 
investigation,  and  more  particularly  so  in  the  case  of  atmospheric  air,  on  account  of  its  interest  in  connection  with 
the  velocity  of  sound.  The  following  table  gives  the  results  of  the  principal  direct  determinations  of  this  ratio  for 
air.  It  may  be  remarked  that  the  methods  most  commonly  employed  have  been  modifications  of  that  employed  by 
Clement  and  Desormes,  and  that  the  chances  of  error  towards  too  small  a  ratio  by  this  method  are  considerable. 


Date. 

Ratio. 

Experimenters. 

Some  of  these  results  are  clearly  too  low  ; 

and  hence  neglecting  all  those  that  fall  be- 

1812 

1-354 

Clement  and  Desormes. 

low  1.39  and  giving  equal  weights  to  the 

— 

1-374 

Gay  Lussac  and  Welter. 

remainder  we  obtain,  with  a  somewhat  large 

1853 

i8s8 

1.249 

1.421 
1.4106 

Delaroche  and  Berard. 
Favre  and  Silbermann. 
Masson. 

probable  error,  the  value  1.4070. 
The  values  obtained  indirectly  from  the 

J859 

1.4025 

Weisbach. 

velocity   of  sound  are  undoubtedly  much 

1861 

1.3845 

Hirn. 

more  accurate,  judged  either  by  the  greater 

1862 

1.41 

Cazin. 

ease  of  the  experiment  or  by   the  better 

1863 
1864 
1864 
1869 

'•399 

1.41 

'•399 

1.302 

Dupre. 
Jamin  and  Richards. 
Tresca  and  Laboulaye. 
Kohlrausch. 

agreement  of  the  results.     Assuming  that 
the  value  332  metres  per  second  is  good  for 
the  velocity  of  sound,  the  ratio  of  the  specific 

f    i873 

1-4053 

Rontgen. 

heats  must  be  near  to   1.4063.      Probably 

1874 

1-397 

Amagat. 

1.4065  may  be  taken  as  fairly  representing 

1883 
1887 

1.4062 
1.384 

Miiller. 
Lummer. 

present  knowledge  of  the  subject. 

*  Variation  assumed  uniform  below  7  with  same  slope  as  from  7  to  5. 
NOTE.  —  For  specific  heats  of  metals,  solids  and  liquids,  see  pp.  294  to  296. 

SMITHSONIAN  TABLES. 

223 


TABLE  23O. 


SPECIFIC    HEAT. 

Specific  Heat  of  Gases  and. Vapors. 


Substance. 

Range  of 
temp.  C.° 

Sp.  ht. 

pressure 
constant. 

Authority. 

Mean 
atio  of 
sp.  hts. 

Authority. 

y 

Acetone  

26-110 

0.3468 

Wiedemann 

- 

- 

"....• 

27-179 

0.3740 

" 

— 

— 

"                         ... 

129-233 

0.4125 

Regnault 

— 

- 

Air          ! 

—  30  to  +  10 

0.23771 

" 

- 

- 

O-IOO 

0.23741 

— 

— 

u                               .... 

O-2OO 

0-237  5  i 

u 

— 

— 

,1 

20-100 

0.2389 

Wiedemann 

_ 

— 

«                  !     !     ! 

mean 

0.23788 

- 

.4066 

Various 

0.1691 

Alcohol,  ethyl         .         .       "T 

108-220 

0-4534 

Regnault 

.136 

(  Jaeger 
(  Neyreneuf 

0.3991 

"        methyl 
Ammonia       .... 

101-223 
23-100 

0.4580 
0.5202 

Wiedemann 

— 

— 

27-200 

0-5356 

" 

— 

— 

"               .... 

24-216 

0.5125 

Regnault 

- 

- 

(  Ccizin 

•    '"•".•    ;  • 

mean 

0.5228 

- 

I-3I 

\  Wullner 

0.3991 

Benzene  

34-H5 

0.2990 

Wiedemann 

- 

- 

"..... 

35-I80 

0-3325 

u 

— 

— 

"                        ... 

116-218 

0-3754 

Regnault 

- 

- 

Bromine  

83-228 
19-388 

0-0555 

Strecker 

1.293 

Strecker 

0.0428 

Carbon  dioxide 

—28  to  +7 

0.1843 

Regnault 

"            "            ... 

15-100 

0.2025 

" 

— 

— 

((                                                  «                                  .               ^           -       -,     "^                               ^ 

11-214 

0.2169 

" 

- 

- 

.        ,        . 

mean 

0.2012 

- 

1.300 

(  Rontgen 
}  Wullner 

0.1548 

Carbon  monoxide  . 

23-99 

0.2425 

Wiedemann 

- 

- 

"       '.-        •        ' 

26-198 

0.2426 

« 

1.403 

j  Cazin 
]  Wullner 

0.1729 

Carbon  disulphide  . 

86-190 

0.1596 

Regnault 

i.  200 

Beyne 

0.1330 

Chlorine          .... 

13-202 

O.I2IO 

ft 

— 

— 

16-343 

O.II25 

Strecker 

'•323 

Strecker 

0.0850 

Chloroform    .... 

27-118 

O.I44I 

Wiedemann 

- 

.... 

28-189 

0.1489 

« 

1.106 

(  Beyme 
}  Muller 

0.1346 

Ether      ..... 

69-224 

0.4797 

Regnault 

_ 

_ 

7            ^ 

27-189 

0.4618 

Wiedemann 

_ 

_ 

" 

25-111 

0.4280 

- 

- 

« 

mean 

0.4565 

_ 

1.029 

Muller 

0.4436 

Hydrochloric  acid  . 

22-214 
13-100 

0.1852 
0.1940 

Regnault 
Strecker 

I-395 

Strecker 

0.1391 

Hydrogen       .... 

—  28  to  +9 

3-3996 

Regnault 

- 

- 

"               .... 

12-198 

3.4090 

If 

— 

— 

"               .... 

21-100 

34100 

Wiedemann 

- 

- 

"               .... 

mean 

3.4062 

— 

1.410 

Cazin 

2.419 

"          sulphide  (HgS) 

20-206 

0.2451 

Regnault 

1.276 

Muller 

0.1925 

Methane          .... 

18-208 

0.5929 

" 

1.316 

" 

0.4505 

1  Nitrogen         .... 

O-2OO 

0.2438 

" 

1.410 

Cazin 

0.1729 

Nitric  oxide  (NO)  . 

13-172 

0.2317 

" 

— 

— 

Nitrogen  tetroxide  (NOs) 

27-67 

1.625 

)  Berthelot 

- 

- 

"                "              " 

27-150 

I.II5 

>  and 

— 

— 

"                "              " 

27-280 

0.650 

)  Ogier 

— 

— 

Nitrous  oxide 

16-207 

O.2262 

Regnault 

— 

- 

«           "              ... 

26-103 

O.2I26 

Wiedemann 

- 

- 

"           "              .         .         . 

27-200 

O.224I 

" 

— 

— 

"           "              . 

mean 

O.22I4 

- 

1.291 

Wullner 

•1715 

Sulphur  dioxide  (SO2)  . 

16-202 

0.1544 

Regnault 

1.26 

\  Muller     J 

0.1225 

Water              . 

128-217 

0.4805 

" 

- 

- 

Macfarlane 

. 

100-125 

0.3787 

Gray 

_ 

_ 

. 

mean 

0.4296 

•" 

1.300 

Various 

0.3305 

SMITHSONIAN  TABLES. 


224 


TABLES  231  ,  232, 


VAPOR    PRESSURE. 


TABLE  231. —Vapor  Pressure  of  Ethyl  Alcohol.* 


0 

d, 

0° 

1° 

2° 

3° 

4°             5° 

6° 

7° 

8° 

9° 

Vapor  pressure  in  millimetres  of  mercury  at  o°  C. 

0° 

10 

20 
30 

12.24 
23.78 
44-00 
78.06 

13.18 

25-3T 
46.66 
82.50 

14.15 
27.94 

49-47 
87.17 

15-16 
28.67 

52-44 
92.07 

16.21 
30-5° 
55-56 
97-21 

3244 
58.86 
102.60 

18.46 
34-49 
62.33 

108.24 

19.68 

36,67 

65-97 
114.15 

20.98 

38.97 
69.80 
120.35 

22.34 
41.40 

73-83 
126.86 

40 

50 
60 
70 

I33-70 
220.00 

350-30 
541.20 

140-75 
230.80 
366.40 

148.10 
242.50 
383-10 
588.35 

155.80 
253.80 
400.40 
613.20 

163.80 
265.90 
4i8.35 
638-95 

172.20 
278.60 

6^55 

iSr.oo 
291.85 

693.10 

190.10 
305.65 
476.45 
721.55 

199.65 
3  '9-95 
497-25 
751.00 

209.60 

334-85 
518.85 

781.45 

From  the  formula  log/  =  a  +  bat  -f  r/3*  Ramsay  and  Young  obtain  the  following  numbers.! 

d 

A 

E 
H 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

Vapor  pressure  in  millimetres  of  mercury  at  o°  C. 

0° 

IOO 

200 

12.24 
1692.3 
22182. 

23-73 
2359.8 
26825. 

43-97 
3223-0 
32196. 

78.11 
4318.7 
38389- 

I33-42 
5686.6 
455*9- 

219.82 
7368.7 

350-21 
9409.9 

540.91 
11858. 

811.81 
14764. 

1186.5 
18185. 

TABLE  232.  — Vapor  Pressure  of  Methyl  Alcohol. % 


0 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

E 
H 

Vapor  pressure  in  millimetres  of  mercury  at  o°  C. 

0° 

29-97 

31.6 

35-6 

35-6 

37-8 

40.2 

42.6 

45-2 

47-9 

50.8 

10 

53-8 

57-0 

60.3 

63.8 

67.5 

71.4 

75-5 

79-8 

84-3 

89.0 

20 

94-o 

99-2 

104.7 

110.4 

116.5 

122.7 

129.3 

136.2 

143-4 

151.0 

30 

40 

158.9 
259.4 

167.1 
271.9 

J75-7 

184.7 

298.5 

194.1 
312.6 

203.9 

327.3 

214.1 

342.5 

224-7 
358.3 

235.8 

374-7 

247.4 
391-7 

£ 

409.4 
624.3 

427.7 
650.0 

&£ 

466.3 
703.8 

486.6 
732.0 

5°7-7 
761.1 

529-5 
791.1 

352-0 
822.0 

575-3 

599-4 

*  This  table  has  been  compiled  from  results  published  by  Ramsay  and  Young  (Jour.  Chem.  Soc.  vol.  47,  and  Phil. 
Trans.  Roy.  Soc.,  1886). 

t  In  this  formula  «  =  5.0720301;   log  b-  1.6406131 ;  log  c-  0.6050854 ;  log  a  =  0.00337  7538;  \ogft  =  1.99682424 
(c  is  negative). 

J  Taken  from  a  paper  by  Dittmar  and  Fawsitt  (Trans.  Roy.  Soc.  Edin.  vol.  33). 
SMITHSONIAN   TABLES. 

225 


TABLE    233. 


VAPOR   PRESSURE.* 

Carbon  Bisulphide,  Chlorobenzene,  Bromobenzene,  and  Aniline. 


Temp. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

(a)   CARBON  BISULPHIDE. 

0° 

127.90 

133.85 

140.05 

146.45 

153-10 

160.00 

167.15 

174.60 

182.25 

190.20 

10 

198.45 

207.00 

215.80 

224.95 

234.40 

244.15 

254.25 

264.65 

275.40 

286.55 

20 

298.05 

309.90 

322.10 

334-70 

347-70 

361.10 

374-95 

389.20 

403.90 

419.00 

3° 

434.60 

450-65 

467-15 

484.15 

501-65 

519.65 

538.15 

557-15 

576.75 

596.85 

40 

617.50 

638.70 

660.50 

682.90 

705.90 

729.50 

753-75 

778.60 

804.10 

830.25 

(b)   CHLOROBENZENE. 

20° 

8.65 

9.14 

9.66 

IO.2I 

10.79 

11.40 

12.04 

12.71 

13.42 

14.17 

3° 
40 

14-95 
25.10 

26:738 

16.63 

27.72 

29.12 

18.47 
30.58 

19-45 
32.10 

20.48 
33-69 

21.56 

35-35 

22.69 
37.08 

23-87 
38.88 

50 

40.75 

42.69 

4472 

46.84 

49-05 

51.35 

53-74 

56.22 

58.79 

61.45 

60 

64.20 

67.06 

70.03 

73-" 

76.30 

79.60 

83.02 

86.56 

90.22 

94.00 

70 

97.90 

101.95 

106.10 

110.41 

114.85 

"9-45 

124.20 

129.10 

I34-i5 

139.40 

80 

144.80 

150.30 

156-05 

161.95 

168.00 

174-25 

181.70 

187.30 

194.10 

201.15 

90 

208.35 

215.80 

223.45 

231.30 

239-35 

247.70 

256.20 

265.00 

274.00 

283.25 

100 

292.75 

302.50 

312.50 

322.80 

333-35 

344.15 

355-25 

366.65 

378.30 

390.25 

1  10 

402.55 

415.10 

427-95 

44i.i5 

454-65 

468.50 

482.65 

497.20 

1  20 

542.80 

558-70 

575-05 

608.75 

626.15 

643-95 

662.15 

68075 

699-65 

130 

718.95 

738.65 

758.80 

— 

— 

— 

— 

— 

(c)   BROMOBENZENE. 

40C 

- 

- 

- 

- 

- 

12.40 

13.06 

J3-75 

14.47 

15.22 

50 

16.00 

16.82 

17.68 

18.58 

19.52 

20.50 

21.52 

22.59 

23-71 

24.88 

60 

26.10 

27.36 

28.68 

30.06 

3i-5o 

33-oo 

34-56 

36.18 

37.86 

39.60 

70 

41.40 

43.28 

45-24 

47.28 

49.40 

51.60 

53-88 

56-25 

61.26 

80 

63.90 

66.64 

69.48 

7242 

75-46 

78.60 

81.84 

85.20 

88'.68 

92.28 

90 

96.00 

99.84 

103.80 

107.88 

112.08 

116.40 

120.86 

125.46 

130.20 

i35-o8 

100 

140.10 

145.26 

1  50-57 

156-03 

161.64 

167.40 

173-32 

179.41 

18^.67 

192.10 

no 

198.70 

205.48 

212.44 

219.58 

226.90 

234.40 

242.10 

250.00 

258.10 

266.40 

120 

130 

274.90 
372-65 

283.65 

292.60 
395-  I0 

301-75 
406.70 

418.60 

320.80 
430-75 

330-70 
443-20 

340.80 
455-9° 

351.15 
468.90 

361.80 
482.20 

140 

495-8o 

509.70 

523.90 

538.40 

553-20 

568.35 

583-85 

599-65 

6i5-75 

632.25 

150 

649.05 

666.25 

683.80 

701.65 

7I9-95 

738.55 

757-55 

776.95 

796.70 

816.90 

(d)  ANILINE. 

80° 

1  8.80 

19.78 

20.79 

21.83 

22.90 

24.00 

25.14 

26.32 

27-54 

28.80 

90 

30.10 

3M4 

32-83 

34-27 

35-76 

37-30 

38-90 

40.56 

42.28 

44.06 

100 

45-90 

47.80 

49.78 

51.84 

53-98 

56.20 

58.50 

60.88 

63-34 

65.88 

110 

68.50 

71.22 

74.04 

76.96 

79-98 

83.10 

86  32 

89.66 

93.12 

96.70 

120 

100.40 

104.22 

108.17 

112.25 

116.46 

120.80 

125.28 

129.91 

134.69 

139.62 

130 

144.70 

149.94 

1  55-34 

160.90 

166.62 

172.50 

178.56 

18480 

191.22 

197.82 

140 

204.60 

211.58 

218.76 

226.14 

23372 

241.50 

249.50 

257.72 

266.16 

274.82 

150 

160 

283.70 
386.00 

292.80 

302.15 
409.60 

3"-75 
421.80 

321.60 
434-30 

447.10 

342.05 
460.20 

352-65 
473.60 

363-50 

487.25 

374.60 
501-25 

170 

515-60 

530.20 

545-20 

560.45 

576.10 

592-05 

608.35 

625.05 

642.05 

659-45 

1  80 

677-15 

695-30 

71375     732-65 

75I-90 

771.5° 

" 

*  These  tables  of  vapor  pressures  are  quoted  from  results  published  by  Ramsay  and  Young  (Jour.  Chem.  Soc. 
vol.  47).    The  tables  are  intended  to  give  a  series  suitable  for  hot-jacket  purposes. 
SMITHSONIAN  TABLES. 

226 


VAPOR    PRESSURE. 

Methyl  Salicylate,  Bromonaphthaline,  and  Mercury. 


TABLE  233, 


Temp. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8°             9° 

(e)  METHYL  SALICYLATE. 

70° 

80 

2.40 
4.60 

2.<8 

4.87 

2.77 
5-15 

2.97 
5-44 

3-18 

5-74 

3-40 
6.05 

3-62 
6-37 

3-85 
6.70 

4.09 

7-05 

4-34 
7.42 

90 

7.80 

8.20 

8.62 

9.60 

9-52 

9-95 

10.44 

10.95 

11.48 

12.03 

100 

12.60 

13.20 

13.82 

14.47 

'S-.^ 

15-85 

16.58 

17-34 

18.13 

18.95 

no 

120 

19.80 

30-25 

20.68 
3r-52 

21.  6O 
32.84 

22.55 
34-21 

23-53 
35-63 

24-55 
37.10 

25.61 
38-67 

26.71 
40.40 

27.85 
41.84 

29.03 
43-54 

130 
140 

45-30 
66.55 

47.12 
69.08 

49-01 
71.69 

50.96 
74-38 

52.97 
77-15 

55-05 
80.00 

57.20 
82.94 

59-43 
85-97 

61.73 
89.09 

64.10 
92.30 

150 

160 

95.60 
I34-25 

99.00 
138-72 

IO2.5O 

H3-31 

106.10 
148.03 

109.80 
152.88 

113.60 

157.85- 

"7-51 
162.95 

121.53 
168.19 

125.66 
!73-56 

129.90 
179.06 

170 

184.70 

190.48 

196.41 

202.49 

208.72 

215.10 

221.65 

228.30 

235-J5 

242.15 

1  80 

249-35 

256.70 

264.20 

271.90 

279.75 

287.80 

296.00 

304-48 

3!3-05 

321.85 

190 

330.85 

340-05 

349-45 

359-05 

368.85 

378.90 

389-  i  5 

399.60 

410.30 

421.20 

200 

2IO 

432.35 
557-50 

443-75 
571-45 

455-35 
585-70 

467.25 
600.25 

479-35 
615-05 

491.70 
630.15 

504-35 
645-55 

517.25 
661.25 

530-40 
677.25 

693.60 

220 

710.10 

727.05 

744-35 

761.90 

779-85 

798.10 

(f)  BROMONAPHTHALINE. 

110° 

3-6o 

3-74 

3-89 

4-05 

4.22 

4.40 

4-59 

4-79 

5-oo 

5.22 

120 

5-45 

5-70 

5-96 

6.23 

6.51 

6.80 

7.10 

7.42 

7-76 

8.12 

130 

8.50 

8.89 

9.29 

9.71 

10.15 

1  0.60 

11.07 

11.56 

12.07 

12.60 

I4O 

13-15 

I3-72 

14-31 

14.92 

15-55 

16.20 

16.87 

17-56 

18.28 

19.03 

150 

19.80 

20.59 

21.41 

22.25 

23.11 

24.00 

24.92 

25.86 

26.83 

27.83 

1  60 

170 

28.85 
40.75 

29.90 
42.12 

30.98 
43-53 

32.09 
44-99 

33-23 
46.50 

34-40 
48.05 

35-60 
49-64 

36-83 
51.28 

38.10 
52.96 

39-41 
54-68 

180 

56-45 

58.27 

60.14 

62.04 

64.06 

66.10 

68.19 

70-34 

72.55 

74.82 

190 

77-15 

79-54 

81.99 

84.51 

87.10 

89-75 

92.47 

95.26 

98.12 

101.05 

200 

210 

104.05 
138.40 

107.12 
142.30 

110.27 
146.29 

113.50 
150-38 

116.81 

J54.57 

1  20.20 
158.85 

123.67 
163-25 

127.22 
167.70 

130.86 
172.30 

134-59 
176-95 

22O 
230 
240 

181.75 
235-95 
303-35 

186.65 
242.05 
310.90 

191.65 
248.30 
318-65 

196.75 
254.65 
326.50 

202.00 
261.20 
334-55 

207-35 
267.85 

342-75 

212.80 
274.65 
35i-io 

218.40 
281.60 
359.65 

224.15 
288.70 
368.40 

230.00 
295-95 
377-3° 

250 

260 

386.35 

487-35 

395.60 
498.55 

405-05 
509.90 

414.65 
521.50 

424.45 
533-35 

434-45 
545-35 

444.65 
557-60 

455-oo 
570.05 

465.60 
582.70 

476.35 
595-60 

270 

608.75 

622.10 

635-70 

649-5° 

663.55 

677-85 

692.40 

707-15 

722.15 

737-45 

(g)  MERCURY. 

270° 

280 
290 

123.92 

157-35 
198.04 

126.97 
161.07 
202.53 

130.08 
164.86 
207.10 

133.26 
168.73 
211.76 

136-5° 
172.67 
216.50 

139.81 
176.79 
221.33 

143.18 
180.88 
226.25 

146.61 
185.05 
231-25 

150.12 
189.30 
236.34 

I53-70 
I93-63 
24I-53 

300 

310 
320 
330 
340 

246.81 
304.93 
373-67 
454.41 
548.64 

252.18 

3"-30 
381.18 
463.20 

558.87 

257.65 
317.78 
388.81 

472.F2 
569-25 

263.21 
324.37 
396.56 
481.19 
579-78 

268.87 
33i-o8 
404.43 
490.40 
590.48 

274.63 

337.89 
412.44 

499-74 
601.33 

280.48 
344.81 
420.58 
509.22 
612.34 

286.43 
35'-85 
428.83 
518.85 
623.51 

292.49 
359-oo 
437.22 
528.63 
634.85 

208.66 
366.28 

445-75 

646.36 

350 

658.03 

669.86 

681.86 

694.04 

706.40 

718.94 

731-65 

744-54 

757-61 

770.87 

360 

784-31 

227 


TABLE  234. 


AIR    AND    MERCURY    THERMOMETERS, 


Rowland  has  shown  (Proc.  Am.  Acad.  Sci.  vol.  15)  that,  when  o°  and  100°  are  chosen  for  fixed  points,  the  relation 
between  the  readings  of  the  air  and  the  mercury  in  glass  thermometers  can  be  very  nearly  expressed  by  an  equation 
of 'the  form  t=T—at(ioo  —  t)(b  —  f), 

where  t  is  the  reading  of  the  air  thermometer  and  T  that  of  the  mercury  one,  a  and  b  being  constants.  The  smaller 
a  is,  the  more  nearly  will  the  thermometers  agree  at  all  points,  and  there  will  be  absolute  agreement  for  t=o  or 
ioo  or  b. 

Regnault  found  that  a  mercury  thermometer  of  ordinary  glass  gave  too  high  a  reading  between  o°  and  100°,  and  too 
low  a  reading  between  100°  and  about  245°.  As  to  some  other  thermometers  experimented  on  by  Regnault, 
little  is  recorded  of  their  performance  between  o°  and  iooj,  but  all  of  them  gave  too  high  readings  above  100°, 
indicating  that  below  100°  the  mercury  thermometer  probably  reads  too  low.  Regnault  states  this  to  be  the 
case  for  a  thermometer  of  Choisy  le  Roi  crystal  glass,  and  puts  the  maximum  error  at  from  one  tenth  to  two  tenths 
of  a  degree.  Regnault's  comparisons  of  the  air  and  mercury  thermometers  and  a  comparison  by  Recknagel  of  a 
mercury  thermometer  of  common  glass  with  the  air  thermometer  are  compared  with  the  above  formula  by  Rowland. 
The  tables  are  interesting  as  showing  approximately  the  error  to  be  expected  in  the  use  of  a  mercury  thermom- 
eter and  the  magnitude  of  the  constants  a  and  b  for  different  glasses.  They  are  given  in  the  following  Table. 
Regnault's  results  above  100°  C.  compared  with  the  formula  /=r  T— at(ioo  —  f) (b  —  t),  give  for  the  constants  a 
and  b  the  following  values  : 

Cristal  de  Choisy  le  Roi      .     a  =  0.00000032,     £rro°. 

Verre  ordinaire    .        .        .     a  =  0.00000034,    £  =  245°. 

Verre  vert    ....     #  =  0.000000095,  £~  —  270°.* 

Verre  de  Suede     .       .        .     a  =  0.000000 14,    £=io°. 

Common  glass  (Recknagel)     a  —  0.00000033,     ^  =  290°. 


(a)  TEMPERATURES  BETWEEN  o°  AND  100°  C. 

There  are  no  observed  results  with  which  to  compare  the  calculations  for  the  Choisy  le  Roi  thermometer 

through  this  range,  and  in  the  case  of  the  verre  ordinaire,  the  specimen  for  which  the  readings  below  100° 
are  given  was  not  the  same  as  that  used  above  100°,  from  which  the  constants  a  and  b  were  calculated.     Row- 

land shows  that  a  =  0.00000044  and  ^  —  260  give  considerably  better  agreement. 

Regnault's  thermometers. 

Recknagel's  thermometer. 

thermome- 

Choisy 

Verre  ordinaire. 

ter 

Calculated. 

Observed. 

Calculated. 

O 

OO.OO 

00.00 

00.00 

OO.OO 

OO.OO 

.OO 

IO 

10.00 

- 

10.07 

- 

10.08 

10.08 

.00 

20 

19.99 

— 

20.  1  2 

- 

20.14 

20.14 

.00 

3° 

30.12 

30.15 

+  -03 

30.18 

30.18 

.00 

40 

30-97 

40.23 

40.17 

—.06 

40.20 

40.20 

.00 

50 

49.96 

50.23 

50'17 

—.06 

50.20 

50.20 

.00 

60 

59-95 

60.24 

60.15 

—.09 

60.  1  8 

60.  1  8 

.00 

70 

69-95 

7O.22 

70.12 

—  .10 

70.14 

70.15 

+  .01 

80 

79.96 

80.10 

80.09 

—  .OI 

80.10 

80.  1  1 

+.01 

90 

89.97 

- 

90.05 

- 

90.05 

90.06 

+  .01 

IOO 

: 

I  OO.OO 

I  OO.OO 

I  OO.OO 

~ 

100.00 

100.00 

+  .0 

(b)  TEMPERATURES  ABOVE  100°  C.,  REGNAULT'S  THERMOMETERS. 

Air 

Choisy  le  Roi. 

Verre  ordinaire. 

Verre  vert. 

Verre  de  Suede. 

ther. 

Obs. 

Calc. 

Diff. 

Obs. 

Calc. 

Diff. 

Obs. 

Calc. 

Diff. 

Obs. 

Calc. 

Diff. 

IOO 

100.00 

I  OO.OO 

+.00 

I  OO.OO 

I  OO.OO 

.OO 

I  OO.OO 

I  OO.OO 

.00 

100.00 

I  OO.OO 

.OO 

120 

I2O.I2 

1  20.09 

+.03 

119-95 

119.90 

+.05 

I2O.O7 

1  20.09 

—  .or 

120.04 

1  20.04 

.OO 

I4O 

140.29 

140.25  +.04 

1  39-85 

139.80 

+.os 

I4O.2I 

140.22 

—  .01 

140.11 

140.10 

+  .01 

160 

160.52 

160.40   +.03 

159-74 

159-72 

+  .02 

160.40 

160.39 

+  .01 

160.20 

1  6o.2  1 

—  .01 

180 

l8o.8o 

180.8- 

—.03 

179.63 

179.68 

—•°5 

l8o.6o 

180.62 

—  .02 

180.33 

180.34 

—  .01 

200 

2OI.25 

301.28 

—•03 

199.70 

199.69 

+  .01 

200.80 

200.89 

—.09 

200.50 

200.53 

—03 

22O 

221.82 

221.86 

—.04 

219.80 

219.78 

+  .02 

221.20 

221.23 

—.03 

220.75 

220.78 

—03 

240 

242.55 

242.56 

—.01 

239.90 

239.96 

—.06 

241.60 

241.63 

—•03 

241.16 

241.08 

+.08 

260 

263.44 

263.46 

—  .02 

260.20 

260.21 

—  .OI 

262.15 

262.09 

+.07 

280 

284.48 

284.52 

—.04 

280.58 

280.00 

—.02 

282.85 

282.63 

+  .22 

300 

30572 

305-76 

—.04 

301.08 

301.12 

—.04 

320 

327-25 

327.20 

—.05 

321.80 

321.80 

.OO 

340 

349-30 

348.88 

+.42 

343-00 

342.64 

+  .36 

SMITHSONIAN  TABLES. 


*  Misprinted  [+]  270  in  Rowland's  paper. 
228 


COMPARISON   OF   THERMOMETERS. 


TABLES  235,  236. 


Chappius  gives  the  following  equations  for  comparing  glass  thermometers: 

iooo(7>-  Ta)  =  .00543  doc-  Tm)  Tm+  i.4I2  X  io-*(ioo2-  Tm*)Tm-  ^323  X  io-«  (I0o*-  Tm*)  T 
iooo(7Vo3-  rff)  =  .o35v(ioo-  Tm)  7'm-o.234  Xio-*(ioo*-  TJ)  Tn-o.5io  X  icH»(i«*-  T*)T\ 
N=  nitrogen  ;  H=  hydrogen  ;  C02  -  carbon  dioxide  ;  m  =  mercury. 

TABLE  235.  -Hydrogen  Thermometer  compared  with  others. 

This  table  gives  the  correction   which  added  to  the  Jhermo^eter  reading  gives  the  temperature  by  the  hydrogen 


Chappius's  experiments.t 

Marek's  experiments.* 

Tempera- 
ture by 

Hard 

Mercury  in  glass. 

hydrogen 
thermom- 
eter. 

French 
glass 
mercury 
ther- 

Nitrogen 
thermome- 
ter. 

Carbon 

dioxide 
thermome- 
ter. 

Hard 

French 

Jena 

Thuringian  glass. 

mometer. 

glass. 

glass. 

glass. 

1830-40. 

1888. 

—  2O 

+0.172 

+0.014 

+0.071 

—  10 

+0.073 

+0.007 

+0.032 

C 

o.ooo 

O.OQO 

0.000 

0.000 

O.OOO 

0.000 

O.OOO 

O.OOO 

IO 

—  0.052 

O.OO6 

—  0.025 

—  0.044 

—  O.o6o 

—  0.056 

—0.086 

—  0.072 

2O 

—  0.085 

—  O.OIO 

—0.043 

—0.073 

—  O  IOO 

—0.091 

—0.149 

—  0.125 

30 

—  0.102 

—  O.OII 

—0.054 

—  0.091 

—0.125 

—  0.109 

—  0.191 

—  0.159 

40 

—  O.IO7 

—  O.OII 

—0.059 

—0.098 

—0.134 

—  O.I  1  1 

—  0.213 

—0.178 

5° 

—  O.IO3 

—0.009 

—0.059 

—0.096 

—  0.132 

—  O.IO3 

—  0.216 

—0.180 

60 

—  O.OQO 

—  0.005 

-0-053 

—0.086 

—  O.IlS 

—0.086 

—  O.2OI 

—0.168 

70 
80 

—0.072 
—  O.O5O 

O.OOI 
+  0.002 

—  0.044 
—  0.030 

—  0.070 
—  0.050 

—0.096 
—0.068 

—  0.064 
—  0.041 

—  O.I7I 
—  O.I27 

—0.143 

—  o.i  06 

90 

—  O.O26 

+0.003 

—  0.016 

—  O.O26 

—0-035 

—O.OlS 

—  0.069 

—  0.058 

100 

0.000 

0.000 

o.ooo 

O.OOO 

O.OOO 

O.OOO 

O.OOO 

o.ooo 

TABLE  236.  —  Air  Thermometer  compared  with  others. 

This  table  gives  the  correction  which  added  to  the  thermometer  reading  gives  the  temperature  by  the  air  thermometer. 


Temperature 
by  air 
thermome- 
ter. 

Mercury  in 
Thuringian 
glass 
thermometer 
(Grommach  §). 

Mercury  in  Jena 
glass  thermome- 
ter (Wiebe  and 
Boucher  ||). 

Temperature 
by  air 
thermome- 
ter. 

Mercury  in  Jena 
glass  thermome- 
ter  (Wiebe  and 
Boucher  ||). 

Temperature 
by  air 
thermome- 
ter. 

Baudin  alcohol 
thermometer 
^WhitelF). 

—  20 

+0.03 

+0.153 

130 

—  O.O7 

O 

—  O.OOO 

—  10 

+0.02 

+0.067 

140 

—  0.09 

—5 

—0.144 

O 

o.oo 

0.000 

150 

—  O.IO 

—  IO 

—0.382 

10 

—  0.03 

—0.049 

160 

—O.IO 

—  15 

—0.704 

20 

—  O.I  I 

—0.083 

170 

—0.08 

—  20 

—  I.  IOO 

3° 

—  0.12 

—  O.IO3 

180 

—  O.o6 

—25 

-1.563 

4° 

—O.OS 

—  O.IIO 

190 

—  O.O2 

—3° 

—2.082 

5° 

—  0.107 

2OO 

+0.04 

—35 

—2.648 

54 
60 

—  O.O4 

—0.096 

2IO 
2  2O 

+0.1  1 
+0.21 

—40 

—45 

3* 

70 

—  O.O6 

—  0.078 

230 
240 

+0.32 
+0.46 

—50 

-4.541 

—  5.206 

82 

—  O.O4 

—0.054 

2|0 
260 

+0.63 

+0.82 

-65 

-5.872 

—  6-531 

90 

_ 

—  0.028 

270 

+  I.O5 

—70 

—7-174 

IOO 

_ 

o.ooo 

280 

+  1.30 

—80 

—8-371 

no 

_ 

—0.03 

20O 

+  I-58 

—90 

—9-392 

1  20 

: 

—  0.05 

300 

+  I.9I 

—  IOO 

—  10.163 

*  These  two  tables  are  taken  with  some  slight  alteration  from  Landolt  and  Boernstein's  "  Phys.  Chem.  Tab." 
t  P.  Chappius,  "Trav.  et  Mem.  du  Bur.  internal,  des  Poids  et  Mes."  vol.  6,  1888. 
t  Marek,  "Zeits.  fur  Inst.-K."  vol.  10,  p.  283.  ?> 

§  Grommach,  "  Metr.  Beitr.  heraus.  v.  d.  Kaiser.  Norm.-Aich.  Comm.     1872. 
||  Wiebe  und  Bbttcher,  "Zeits.  fur  Inst.  K."  vol.  10,  p.  233. 
IT  White,  "  Proc.  Am.  Acad.  Sci."  vol.  21,  p.  45. 

SMITHSONIAN   TABLES. 

229 


TABLE  237, 


CHANCE  OF  THERMOMETER  ZERO  DUE  TO  HEATING.* 

When  a  thermometer  is  used  for  measurements  extending  over  a  range  of  more  than  a  few  degrees,  its  indications  are 
generally  in  error  due  to  the  change  of  volume  of  the  glass  lagging  behind  the  change  of  temperature.  Some  data 
are  here  given  to  illustrate  the  magnitude  of  the  change  of  zero  after  heating.  This  change  is  not  permanent,  but 
ihe  thermometer  may  take  several  days  or  even  weeks  to  return  to  its  normal  reading. 


1  



Kind  of  glass. 

No.  of 
experi- 
ment. 

Maximum 
temp,  in 
deg.  cent. 

Time  at 
maximum 
temp,  in 
hours. 

Normal  Jena  glass. 

Thuringian 
glass. 

Composition  of 
Jena  glass 
used. 

I. 

II. 

Depression  of  freezing-point. 

I 

290 

5 

1.0 

1.0 

2.1 

ZnO      7     % 

2 

290 

5 

i«3 

I.c 

2.7 

CaO      7     % 

3 

290 

5 

I* 

i-7 

Na20  14.5  % 

4 

290 

5 

1.6 

1.8 

3-4 

A1203    2.5% 

i 

290 
290 

5 

5 

1.8 

1.9 

2.0 

3-6 

3-7 

B203     2     % 
SiO2    67     % 

7 

290 

25 

2.0 

2.2 

4.2 

TABLE  238. 

CHANCE  OF  THERMOMETER  ZERO  DUE  TO  HEATINC.t 


Ratio  of  soda  and  potash 
in  the  glass. 

Depression  of 
zero  due  to 

Description  of  thermometer. 

manufacture. 

one  hour's 
heating  to 

Na2O/K2O 

K2O/Na20 

100°  C. 

Humboldt,  No.  2     .... 

Before  1835 

0.04 

. 

O.O6 

J.  G.  Greiner,  FI 

1848 

0.08 

_ 

0.15 

"         F2     .        .        .        . 

1856 

0.22 

- 

0.38 

"        F3 

1872 

— 

O.2I 

0.38 

Ch.  F.  Geissler,  No.  13  . 

1875 

_ 

O.26 

0.40 

G.  A.  Schultze,  No.  3      . 

1875 

_ 

0.24 

0.44 

Rapp's  Successor,  F* 

1878 

" 

0.83 

0.65 

*  Allihn,  "Zeits.  fiir  Anal.  Chem.';  vol.  29,  p.  385. 

t  W.  Fresenius,  "Zeits.  fur  Anal.  Chem."  vol.  27,  p.  189.  See  also,  for  this  and  following  table,  Wiebe  in  the 
"Zeitschrift  fiir  Instrumentenkunde,"  vol.  6,  p.  167,  from  which  Fresenius  quotes.  The  thermometer  referred  to  im 
this  table  belonged  to  the  Kaiserlichen  Normal-Aichungs  Commission. 

SMITHSONIAN  TABLES. 

230 


TABLE  239. 

EFFECT  OF  COMPOSITION  ON  THERMOMETER  ZERO.* 

Jena  Glasses. 


Depression  of 

Descriptive 
number. 

Si2O 

Na20 

K20 

CaO 

A1203 

B203 

ZnO 

zero  due  to 
one  hour's 

heating  to 

100*  C. 

IV 

70 

_ 

13-5 

16.5 

_ 

_ 

_ 

0.08 

VIII 

70 

IS 

1S 

_ 

_ 

_ 

0.08 

XXII 

66 

14 

14 

6 

_ 

_ 

_ 

1.05 

XXXI 

66 

II.  I 

16.9 

6 

_ 

_ 

_ 

I.O3 

XVII111 

69 

15 

10.5 

- 

5 

_ 

_ 

1.  06 

XX111 
XIV111 

70 
69 

7-5 
H 

7-5 

15 

7 

i 

2 

7 

0.17 
0.05 

t  XVI111 

67-5 

14 

_ 

7 

2.5 

2 

7 

0.05 

XVIII 

52 

9 

9 

30 

0.05 

TABLE  24O. 
CHANCE    OF  ZERO  OF  THERMOMETER  WITH  TIME. 

Closely  allied  to  the  changes  illustrated  in  Tables  235-237  is  the  slow  change  of  volume  of  the  bulb  of  a  thermometer 
with  age.     The  following  short  table  shows  the  change  for  the  normal  Jena  thermometer.* 


Date  of  observation. 

Thermometer 
number. 

1886 

1889 

1890 

Total 
rise. 

Rise  of  zero. 

106 

O.OO 

o-3 

0.04 

O.O4 

108 

O.OI 

O.2 

0.04 

0.03 

665 

O.OI 

o-3 

0.05 

0.04 

6675 
668 

O.O2 
0.02 

0.4 

o-5 

0.05 
0.06 

0.03 
0.04 

670 

O.OO 

o-3 

0.04 

0.04 

671 
672 

O.O5 
0.05 

0.9 

0.8 

0.09 
0.08 

0.04 
0.03 

SMITHSONIAN  TABLES. 


*  Fresenius,  "  Zeits.  fur  Anal.  Chem."  vol.  27,  p.  189. 

t  Normal  Jena  glass. 

$  Allihn,  "  Zeits.  fur  Anal.  Chem."  vol.  29,  P-  385- 

231 


TABLE  241 . 


CORRECTION    FOR   TEMPERATURE    OF    MERCURY    IN    THERMOMETER 

STEM.* 

^  =  ^—0.0000795  n  (t'  —  t),  in  Fahrenheit  degrees;  T—t  —0.000143  »  (/'  —  t),  in  Centigrade  degrees.  Where 
7'=  corrected  temperature,  f=.  observed  temperature,  /'=mean  temperature  of  glass  stem  and  mercury  column, 
«  =  the  length  of  mercury  in  the  stem  in  scale  degrees. 


(a)  CORRECTION  FOR  FAHRENHEIT  THERMOMETER 

—  value  of  0.0000795  «  (/'  —  t). 

t'—t 

10° 

20  = 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

100° 

10° 

O.OI 

O.O2 

0.02 

0.03 

0.04 

0.05 

0.06 

0.06 

• 
0.07 

0.08 

20 

0.02 

O.O3 

O.O5 

0.06 

O.o8 

O.IO 

O.I  I 

0.13 

0.14 

0.16 

30 

O.O2 

O.O5 

O.O7 

O.IO 

0.12 

0.14 

0.17 

0.19 

0.21 

0.24 

40 

O.O3 

O.O6 

O.IO 

0.13 

0.16 

0.19 

O.22 

0.25 

0.29 

0.32 

5° 

O.O4 

0.08 

0.12 

O.IO 

O.2O 

0.24 

0.28 

0.32 

0.36 

0.40 

60 

70 

0.05 
O.O6 

O.IO 
O.I  I 

O.I4 
0.17 

0.19 
O.22 

0.24 
0.28 

0.29 
o-33 

o-33 
o-39 

0.38 
0-45 

0-43 
0.50 

0.48 
0.56 

80 

O.O6 

0.13 

0.19 

0.25 

0.32 

0.38 

0-45 

0.51 

0.57 

0.64 

90 

IOO 

O.O7 
0.08 

0.14 
0.16 

O.2I 
0.24 

0.29 

0.32 

0.36 
0.40 

o-43 
0.48 

0.50 
0.56 

0.57 
0.64 

0.64 

0.72 

0.72 
0.79 

110 

O.OQ 

0.17 

0.26 

o-35 

0.44 

0.52 

0.61 

0.70 

0-79 

0.87 

1  20 

O.IO 

0.19 

O.29 

0.38 

0.48 

o-57 

0.67 

0.76 

0.86 

0.95 

130 

O.IO 

O.2I 

0.31 

0.41 

0.52 

0.62 

0.72 

0.83 

o-93 

1.03 

Ob)  CORRECTION  FOR  CENTIGRADE  THERMOMETER 

—  value  of  0.000143  «  (f1  —  f). 

n 

t'  —  t 

10°               20°               30° 

40° 

50°                60°                70°              80° 

10° 

20 

o.oi            0.03            0.04 
0.03             0.06            0.09 

0.06 
O.I  I 

0.07             0.09            o.io           o.i  i 

O.I4                 O.I7                 O.2O                0.23 

3° 
40 

5° 

0.04             0.09             0.13 
0.06            o.i  i             0.17 

O.O7                  O.I4                  O.2I 

0.17 
0.23 

0.29 

0.21             0.26            0.30           O-34 
0.29             0.34             0.40            0.46 

0.36          0.43          0.50         0.57 

60 

70 
80 
90 

IOO 

0.09                 0.17                 0.26 
O.IO                 O.2O                 0.30 

o.i  i            0.23            0.34 

0.13                 0.26                 0.39 
0.14                 0.29                 0.43 

o-34 
0.40 
0.46 
0.51 

o-57 

0.43           0.51           0.60          0.69 
0.50           0.60           0.70          0.80 
0.57           0.69           0.80          0.92 
0.64             0.77             0.90            1.03 
0.72            0.86             i.oo            1.14 

N.  B.  —  When  t>  —  t  is  negative  the  correction  becomes  additive. 

SMITHSONIAN  TABLES. 


*  "  Smithsonian  Meteorological  Tables,"  p.  12. 
232 


TABLE  241 


CORRECTION    FOR   TEMPERATURE    OF   MERCURY   IN   THERMOMETER 

STEM. 


(c)  CORRECTION  TO  BE  ADDED  TO  THERMOMETER  READING.* 

t  —  t< 

ti 

70° 

80° 

90° 

100° 

120° 

140° 

160° 

180° 

200° 

220° 

n 

10° 

O.O2 

0.03 

0.05 

0.07 

o.n 

0.17 

0.21 

0.27 

o-33 

0.38 

10° 

20 

O.I3 

0.15 

0.18 

0.22 

0.29 

0.38 

0.46 

°-53 

0.61 

0.67 

20 

3° 

0.24 

0.28 

0.33 

0-39 

0.48 

0.£9 

0.70 

0.78 

0.88 

0.97 

3° 

40 

°-35 

0.41 

0.48 

0.56 

0.68 

0.82 

0.94 

1.04 

1.16 

1.28 

40 

50 

0.47 

o-53 

0.62 

0.72 

0.88 

1.03 

I.I7 

I-3I 

1.44 

i-59 

50 

60 

o.|7 

0.66 

0.77 

0.89 

1.09 

1.25 

1.42 

1.58 

1.74 

1.90 

60 

70 

0.69 

0.79 

0.92 

1.  06 

1.30 

1.47 

1.67 

1.86 

2.04 

2.23 

70 

80 

0.80 

0.91 

1.05 

1.  21 

1.52 

1.71 

1-94 

2.15 

2-33 

2-55 

80 

90 

0.91 

1.04 

1.19 

I.38 

'•73 

I.96 

2.20 

2.42 

2.64 

2.89 

90 

IOO 

i.  02 

1.18 

i-35 

I.56 

1.97 

2.18 

2-45 

2.70 

2.94 

3-23 

IOO 

no 

— 

— 

I.78 

2.19 

2-43 

2.70 

2.98 

3.26 

3-57 

1  10 

120 

- 

- 

- 

1.98 

2-43 

2.69 

2-95 

3-26 

3-58 

3-92 

1  20 

130 

- 

- 

- 

- 

2.68 

2.94 

3.2O 

3-56 

3-89 

4-28 

130 

140 

- 

- 

- 

- 

2.92 

3.22 

347 

3-86 

4.22 

4.64 

140 

T 

- 

- 

- 

- 

- 

3-74 

4-i| 

4-56 

5.01 

'5° 

160 

— 

— 

— 

— 

— 

— 

4.00 

4.46 

4.90 

5-39 

160 

170 

1  80 

- 

: 

- 

- 

- 

- 

4.27 
•  4-54 

4.76 
5-°7 

5-24 
5-59 

5-77 
6.15 

170 

1  80 

190 

— 

— 

— 

— 

— 

— 

5-38 

5-95 

6-54 

190 

200 

— 

— 

- 

— 

— 

— 

— 

5-70 

6.30 

6.94 

200 

210 

- 

- 

- 

- 

- 

- 

- 

_ 

6.68 

7-35 

210 

220 

7.04 

7-75 

220 

*  This  table  is  quoted  from  Rimbach's  results,  "Zeit.  fur  Instrumentenkunde,"  vol.  TO,  p.  153.  The  numbers 
represent  the  correction  made  by  direct  experiment  for  thermometers  of  Jena  glass  graduated  from  o°  to  360°  C., 
the  degrees  being  from  i  to  1.6  mm.  long.  The  first  column  gives  the  length  of  the  mercury  in  the  part  of  the  stem 
which  is  exposed  in  the  air,  and  the  headings  under  t  —  t1  give  the  difference  between  the  observed  temperature  and 
that  of  the  air. 


SMITHSONIAN  TABLES. 


233 


TABLES  242,  243. 


EMISSIVITY. 


TABLE  242.  —  Emissivity  at  Ordinary  Pressures. 

According  to  McFarlane*  the  rate  of  loss  of  heat  by  a  sphere 
placed  in  the  centre  of  a  spherical  enclosure  which  has  a 
blackened  surface,  and  is  kept  at  a  constant  temperature  of 
about  14°  C.,  can  be  expressed  by  the  equations 

e  =  .000238  +  3.06  X  io-«V  — 2.6  X  io-8/2, 
when  the  surface  of  the  sphere  is  blackened,  or 

e  —  .000168  +  1.98  X  ioH»*  —  1.7  X  io-8/2, 

when  the  surface  is  that  of  polished  copper.  In  these  equa- 
tions e  is  the  emissivity  in  c.  g.  s.  units,  that  is,  the  quantity 
of  heat,  in  therms,  radiated  per  second  per  square  centimetre 
of  surface  of  the  sphere,  per  degree  difference  of  tempera- 
ture t,  and  t  is  the  difference  of  temperature  between  the 
sphere  and  the  enclosure.  The  medium  through  which 
the  heat  passed  was  moist  air.  The  following  table  gives 
the  results. 


Differ- 
ence of 
tempera- 
ture 
* 

Value  of  e. 

Ratio. 

Polished  surface. 

Blackened  surface. 

5 

.000178 

.000252 

.707 

10 

.OOOl86 

.000266 

.699 

15 

.000193 

.000279 

.692 

20 

.OOO2OI 

.000289 

.695 

25 

.OOO2O7 

.000298 

.694 

30 

.000212 

.000306 

•693 

35 

.OOO2I7 

.000313 

•693 

40 

.000220 

.000319 

•693 

45 

.000223 

.000323 

.690 

5° 

.OOO225 

.000326 

.690 

55 

.000226 

.000328 

.690 

60 

.OOO226 

.000328 

.690 

TABLE  243.— Emissivity  at  Different  Pres- 
sures. 

Experiments  made  by  J.  P.  Nicol  in  Tait's  Labo- 
ratory show  the  effect  of  pressure  of  the  en- 
closed air  on  the  rate  of  loss  of  heat.  In  this 
case  the  air  was  dry  and  the  enclosure  kept  at 
about  8°  C. 


Polished  surface. 

Blackened  surface. 

t 

et 

t 

et 

PRESSURE  76  CMS.  OF  MERCURY. 

63.8 

5°-5 
44-8 

.00987 
.00862 
.00736 
.00628 

6l.2 
50.2 
41.6 

34-4 

.01746 
.01360 
.01078 
.00860 

40-5 

.00562 

27-3 

.00640 

34-2 

.00438 

20.5 

•00455 

29.6 

.00378 

23-3 

.00278 

- 

- 

18.6 

.OO2IO 

" 

~ 

PRESSURE  10.2  CMS.  OF  MERCURY. 

67.8 

.00492 

62.5 

.01298 

61.1 

•00433 

57-5 

.01158 

55 

•00383 

53-2 

.01048 

49-7 

.00340 

47-5 

.00898 

44.9 

.00302 

43-° 

.00791 

40.8 

.00268 

28.5 

.00490 

PRESSURE  i  CM.  OF  MERCURY. 

65 

.00388 

62.5 

.01182 

60 

•00355 

57-5 

.01074 

50 

.00286 

54-2 

.01003 

40 

.00219 

41.7 

.00726 

3° 

.00157 

37-5 

.00639 

23-5 

.00124 

34-0 

.00569 

- 

27-5    . 

.00446 

24.2 

.00391 

SMITHSONIAN  TABLES. 


*  "  Proc.  Roy.  Soc."  1872. 

t  "  P.roc.  Roy.  Soc."  Edinb.  1869. 


234 


TABLES  244,  245, 


EMISSIVITY. 


TABLE  244.  -  Constants  of  Emissivity. 

The  constants  of  radiation  into  vacuum  have  been  determined  for  a  few  substances.  The 
object  of  several  of  the  investigations  has  been  the  determination  of  the  law  of  variation  with 
temperature  or  the  relative  merits  of  Dulong  and  Petit's  and  of  Stefan's  law  of  cooling. 

Dulong  and  Petit's  law  gives  for  the  amount  of  heat  radiated  in  a  given  time  the  equation 


where  A  is  a  constant  depending  on  the  units  employed  and  on  the  nature  of  the  surface,  s  the 
surface,  a  a  constant  determined  by  Dulong  and  Petit  to  be  1.0077,  0  tne  absolute  temperature 
of  the  enclosure,  and  t  the  difference  of  temperature  between  the  hot  surface  and  the  enclosure. 
The  following  values  of  A  are  taken  from  the  experiments  of  W.  Hopkins,  the  results  being 
reduced  to  centimetre  second  units,  and  the  therm  as  unit  of  heat. 

Glass      ......     A  =  .00001327 


Dry  chalk 
Dry  new  red-sandstone 
Sandstone  (building)  . 
Polished  limestone  .  . 
Unpolished  limestone 
(same  block)  .  .  . 

Stefan's  law  is  expressed  by  the  equation 


A  ==.00001195 
A  =  .00001162 
A  =  .00001232 
A  =  .00001263 

A  =  .0001777 


where  //"and  s  have  the  same  meaning  as  above,  a  is  a  constant,  called  Stefan's  radiation  con- 
stant, T\  is  the  absolute  temperature  of  the  radiating  body  and  TO  the  absolute  temperature  of 
the  enclosure.  Stefan's  constant  would  represent,  if  the  law  held  to  absolute  zero,  the  amount 
of  heat  which  would  be  radiated  per  unit  surface  from  the  body  at  i°  absolute  temperature  to 
space  at  absolute  zero.  The  experiments  of  Schleiermacher,  Bottomley,  and  others  show  that 
this  law  approximates  to  the  actual  radiation  only  through  a  limited  range  of  temperature. 


Graetz  *  finds  for  glass 


=  400,  TO  =  O,<T  =  I .0846  X 


Schleiermacher  t  find  for  polished  platinum  wire     •  \  %-[?£  %~%1~%$%SZ 
For  copper  oxide       ...       .     '.^       .  j  %-t^  £0  =  0.  ,  =  0.600  x  .o£ 


TABLE  245.  — Effect  of  Absolute  Temperature  of  Surface. 

The  following  tabular  results  are  given  by  Bottomley.  t  The  results  of  Schleiermacher  were  calculated  from  data  given 
in  the  paper  above  quoted.  The  temperatures  tv  are  in  degrees  centigrade,  and  e  is  the  emissivity  or  amount  of 
heat  in  therms  radiated  per  square  centimetre  of  surface  per  degree  difference  of  temperature  between  the  hot  body 
and  the  enclosure.  The  results  are  all  for  high  vacuum. 


Schleiermacher's  results.     Temperature  of  enclosure,  o°  C.     tvev,  ttf»,  refer  to 
polished  platinum  wire,  fge3  to  blackened  platinum  wire. 

Bottomley's     results     for 
polished     platinum,     the 
enclosures  being  at  15°  C. 

'i 

«\ 

'2 

e*. 

'3 

e* 

* 

e 

130 

21.  6  X  io~6 

6S 

14.5  X  lO-6 

16 

60.9  X  io~6 

302 

65.05  X  lo-6 

2OO 

30.0    " 

no 

l8.7      « 

18 

67.6        ' 

425 

120.3      " 

337 

53-8     " 

232 

32.2      ' 

92 

837        ' 

613 

282.0      " 

137.0    " 

383 

6l.6      " 

228 

147.0 

744 

537-o      " 

826 

3i5-o    " 

740 

198.0     " 

403 

293.0 

806 

653-o 

900 

358.0     « 

585 

540.0 

SMITHSONIAN   TABLES. 


*  "  Wied.  Ann."  vol.  n,  p.  297. 
t  "  Wied.  Ann."  vol.  26,  p.  305. 
t  "  Phil.  Trans.  Roy.  Soc."  1887,  p.  429. 

235 


TABLES  246,  247. 


EMISSIVITY. 


TABLE  246.—  Radiation  of  Platinum  Wire  to  Copper  Envelope. 


Bottomley  gives  for  the  radiation  of  a  bright  platinum  wire  to  a  copper  envelope  when  the  space  between  is  at  the 
highest  vacuum  attainable  the  following  numbers  :  — 

/  =  4.o8°  C.,  <tf  =  378.8  X  iQ—4,  temperature  of  enclosure  16°  C. 

t=  505°  C.,  et—  726.1  X  io-*,          "  "          17°  C. 

It  was  found  at  this  degree  of  exhaustion  that  considerable  relative  change  of  the  vacuum  produced  very  small 
change  of  the  radiating  power.  The  curve  of  relation  between  degree  of  vacuum  and  radiation  becomes  asymp- 
totic for  high  exhaustions.  The  following  table  illustrates  the  variation  of  radiation  with  pressure  of  air  in 
enclosure. 


Temp,  of  enclosure  16°  C.,  /zr4o80  C. 

Temp,  of  enclosure  17°  C.,  t  =  505°  C. 

Pressure  in  mm. 

et 

Pressure  in  mm. 

et 

740. 

8137.0  X  icr4 

0.094 

1688.0  X  IO-4 

440. 

7971.0     " 

•053 

1255.0      « 

140. 

7875.0     ' 

•034 

II26.0      " 

42. 

7591.0     ' 

.013 

920.4      " 

4- 
0.444 

6036.0     " 
2683.0    " 

.0046 
.00052 

831.4      « 
767.4      « 

.070 

1045.0    " 

.OOOI9 

746.4      " 

•034 

.012 

727.3    " 
539-2    « 

Lowest   reached    ) 
but  not  measured  ) 

726.1       " 

.OO5I 

436.4    " 

.00007 

378.8    « 

TABLE  247.  — Effect  of  Pressure  on  Radiation  at  Different  Temperatures. 

The  temperature  of  the  enclosure  was  about  15°  C.     The  numbers  give  the  total  radiation  in  therms  per  square  cen- 
timetre per  second. 


Pressure  in  mm. 

Temp,  of 

wire  in  C°. 

10.0 

I.O 

0.25 

0.025 

About 
o.i  M. 

100° 

0.14 

O.I  I 

0.05 

O.OI 

0.005 

300 

•31 

•50 

d 

.11 

.18 

.02 
.04 

•°°55 
.0105 

•75 

•53 

•25 

.07 

.025 

500 
6oO 

•33 

.13 

•°55 

7OO 

•85 

•45 

•23 

•13 

800 

"• 

•37 

.24 

900 

- 

- 

- 

.56 

.40 
.61 

f  °7Eu  ~^n  interestin*  examp!e  (because  of  its  practical  importance  in  electric  light- 
ing) of  the  effect  of  difference  of  surface  condition  on  the  radiation  of  heat  is  given  oiTthe 
nty  of  Mr.  Evans  and  himself  in  Bottomless  paper.     The  energy  required  to  keep 
up  a  certain  degree  of  mcandescence  in  a  lamp  when  the  filament  is  dull  black  and  when 
with  coating  of  hard  bright  carbon,  was  found  to  be  as  follows  :  - 

Dull  black  filament,  57.9  watts. 

Bright  "           «        39.8  watts. 

SMITHSONIAN  TABLES.                                                 "  1 

236 


TABLE  248. 


PROPERTIES   OF   STEAM. 

Metric  Measure. 

The  temperature  Centigrade  and  the  absolute  temperature  in  degrees  Centigrade,  together  with  other  data  for  steam 
or  water  vapor  stated  in  the  headings  of  the  columns,  are  here  given.  The  quantities  of  heat  are  in  therms  or  calo- 
ries according  as  the  gramme  or  the  kilogramme  is  taken  as  the  unit  of  mass. 


u 

H 

a 
£ 

V 

1 

Pressure  in  mm. 
of  mercury. 

Pressure  in 
grammes  per  sq. 
centimetre  =/. 

Pressure  in 
atmospheres. 

Total  heat  of  evap-  1 
oration  from  o°  at  1 
£=£ 

"S 
'3 
.2* 

ill 

rt 

I* 

(t   \ 

>   \ 
v  J 

^  \\ 

!•! 

Outer  latent  or  ex-  1 
ternal-work  heat 
=  Afiv.*  \ 

Total  heat  of 
steam  =//—  Apv.  I 

Inner  latent  or  in-  II 
ternal-work  heat 
=H—(h  +  Apv).\\ 

Litres  per  gramme,  1 
or  cubic  metres 
per  kilog.  rr  v. 

Ratio  of  inner  la- 
tent heat  to  vol- 
ume of  steam.  t 

0° 

273 

4.60 

6.25 

0.006 

606.5 

0.00 

606.5 

31.07 

575-4 

575-4 

210.66 

2-732 

5 

278 

6-53 

8.88 

.009 

608.0 

5.00 

603.0 

31-47 

576.5 

57L5 

I50.23 

3.805 

10 

283 

9.17 

12.47 

.OI2 

609.5 

IO.OO 

599-5 

31.89 

577-7 

567-7 

108,51 

5-231 

15 

288 

12.70 

17.27 

.017 

DILI 

15.00 

596.0 

32.32 

578.8 

563-7 

79-35 

7.104 

20 

293 

17-39 

23.64 

.023 

612.6 

2O.OI 

592.6 

32.75 

579-8 

559-8 

78.72 

9-532 

25  298 

23-55 

32.02 

0.031 

614.1 

25.02 

589.1 

33-20 

580.9 

555-9 

43-96 

12.64 

3°  303 

3J-55 

42.89 

.042 

615.6 

30.03 

585.6 

33-66 

582.0 

552-0 

33-27 

16.59 

35  308 

41.83 

56-87 

•055 

617.2 

35-°4 

582.1 

34.12 

583-1 

548.2 

25.44 

21.54 

54-91 

74-65 

.072 

618.7 

40.05 

587.6 

34-59 

584.1 

544-1 

19.64 

27.70 

45 

318 

7i-39 

97.06 

.094 

62O.2 

45-07 

57  5-  r 

35-06 

585.2 

540.1 

*S-3l 

35-26 

5° 

323 

91.98 

125.0 

O.I2I 

621.7 

50.09 

571-7 

35-54 

586.2 

536.1 

12.049 

44.49 

55   328 

117.47 

J59-7 

.155 

623.3 

55-n 

568.2 

36.02 

587-2 

532.1 

9.561 

55-65 

60 

333 

148.79 

202.3 

.196 

624.8 

60.13 

564-7 

36-51 

588.3 

528.1 

7-653 

69.02 

65 

338 

186.94 

254.2 

.246 

626.3 

65-17 

561.1 

37.00 

589-3 

524.2 

6.171 

84.94 

70 

343 

233.08 

316.9 

.306 

627.8 

70.20 

557-6 

3748 

590-4 

520.2 

5.014 

103-75 

75 

348 

288.50 

392.3 

0.380 

629.4 

75-24 

554-1 

37-96 

59M 

516.2 

4.102 

125-8 

80 

354-62 

482.1 

.446 

630.9 

80.28 

550.6 

38.42 

592.5 

512.2 

3-379 

85 
90 

95 

I 

433-oo 
633-69 

588.7 
714.4 
861.7 

iS 

.834 

632.4 
633.9 

85-33 
90.38 

95-44 

547-1 
543-6 
540.0 

38.88 

39-33 
39.76 

593-5 
594-6 
595-7 

508.2 
504.2 
500.3 

2.800 
2-334 
1-957 

181.5 
216.0 
255-7 

100 

373 

760.00 

!033- 

I.OOO 

637.0 

100.5 

536.5 

40.20 

596.8 

496-3 

1.6496 

300.8 

105 

378 

906.41 

1232. 

•193 

638.5 

105.6 

533-o 

40.63 

597-9 

492-3 

I-3978 

352.2 

no 

383 

1075.4 

1462. 

.415 

640.0 

uo.6 

529.4 

41.05 

599-o 

488.4 

1.1903 

410.3 

"5 

388 

1269.4 

1726. 

.670 

641.6 

II5-7 

525.8 

41.46 

600.1 

484.4 

1.0184 

475-6 

1  20 

393 

2027. 

.962 

643.1 

I2O.8 

522.3 

41.86 

601.2 

480.4 

0.8752 

549-0 

125 

398 

1/43-9 

2371. 

2.295 

644.6 

125.9 

518-7 

42.25 

602.4 

476.5 

0-7555 

630.7 

130 

403 

2030.3 

2760. 

2.671 

646.1 

131.0 

5T5-I 

42.63 

603-5 

472-5 

0.6548 

721.6 

«35 

140 

408 
413 

2353-7 
2717.6 

3200. 
3695- 

3-097 
3.576 

6477 
649.2 

136.1 
141.2 

511.6 
508.0 

43.01 
43-38 

604.7 
605.8 

468.6 
464.6 

0.5698 
0-4977 

822.3 
933-5 

r45 

418 

4249. 

4.113 

650.7 

146.3 

504-4 

43-73 

607.0 

460.7 

04363 

1055.7 

150 

423 

3581-2 

4869. 

4.712 

652.2 

I5I>5 

500.8 

44.09 

608.2 

4567 

0-3839 

1190. 

J55 

428 

4088.6 

5589- 

653.8 

'56-5 

497-2 

44-43 

609.3 

452-8 

0-3388 

1336. 

1  60 

433 

4651.6 

6324. 

6.  1  20 

161.7 

493-5 

44.76 

610.5 

448.8 

0.3001 

1496. 

165  1438 

5274-5 

7171. 

6.940 

656^8 

166.9 

489.9 

45-09 

611.7 

444.8 

0.2665 

1669. 

170 

443 

596r-7 

8105. 

7-844 

658.3 

172.0 

486.3 

45-40 

612.9 

440-9 

0-2375 

1856. 

I75 

448 

6717.4 

9J33- 

8.839 

659.9 

177.2 

482.7 

45-71 

614.2 

436-9 

O.2I22 

2059. 

1  80 

453 

7546-4 

10260. 

9.929 

661.4 

182.4 

479-0 

46.01 

615.4 

433-0 

O.I90I 

2277. 

•185 

8453-2 

11490. 

11.123 

662.9 

187.6 

475-3 

46.30 

616.6 

429.0 

0.1708 

2512. 

190 
195 

468 

9442-7 
10520. 

12838. 
14303- 

12.425 
13.842 

664.4 

666.0 

192.8 
198.0 

47  T  -7 
468.0 

46.59 
46.86 

617.9 
619.1 

425.0 
421.1 

0.1538 
0.1389 

2763. 

200 

473 

11689. 

15892. 

15-380 

667.5 

203.2 

464-3 

47.13 

620.4 

417.1 

0.1257 

33-8. 

t  = 


Where  A  is  the  reciprocal  of  the  mechanical  equivalent  of  the  thermal  unit. 

+  Afiv)_        internal-work  pressure  Where  y  is  taken  in  Htres  thfi  pressure  is  given  per  square 

11  mechanical  equivalent  of  heat 

decimetre,  and  where  v  is  taken  in  cubic  metres  the  pressure  is  given^per  square  metre,  — the  mechanical  equivalent 
being  that  of  the  therm  and  the  kilogramme-degree  or  calorie  respectively. 

SMITHSONIAN  TABLES. 

237 


TABLE  249. 


PROPERTIES  OF  STEAM, 

British  Measure. 


The  quantities  given  in  the  different  columns  of  this  table  are  sufficiently  explained  by  the  headings.  The  abbrevia- 
tion B.  T.  U.  stands  for  British  thermal  units.  With  the  exception  of  column  3,  which  was  calculated  for  this 
table,  the  data  are  taken  from  a  table  given  by  Dwelshauvers-Dery  (Trans.  Am.  Soc.  Mech.  Eng.  vol.  xi.). 


14 

Pressure 
in  pounds  per 
square  foot. 

Pressure  in 
atmospheres. 

i^ 
jo 

Volume  per 
pound  in  cubic 
feet. 

It 

k 

~l^ 

PH 

11 
sis 

III* 

C    $£      • 

External  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

Total  latent 
heat  per  pound 
of  steam  in 
B  T.  U. 

tl 
III 

1 

I44 

0.068 

102.0 

334.23 

0.0030 

70.1 

980.6 

62.34 

1043. 

1113.0 

2 

288 

.136 

126.3 

'73-23 

.0058 

94-4 

961.4 

64.62 

IO26. 

1  1  20.4 

3 

432 

.204 

I4I.6 

117.98 

.0085 

109.9 

949-2 

66.58 

ion. 

1127.0 

4 

576 

.272 

I53-1 

89.80 

.01  1  1 

121.4 

940.2 

67.06 

1007. 

1128.6 

5 

720 

.340 

162.3 

72.50 

.0137 

I30-7 

932.8 

67.89 

IOOI. 

1131.4 

6 

864 

0.408 

170.1 

61.10 

0.0163 

138.6 

926.7 

68.58 

995-2 

"33-8 

7 

1008 

476 

176.9 

53-oo 

.0189 

145-4 

921.3 

69.18 

990-5 

"35-9 

8 
9 

II52 
1296 

•544 
.612 

182.9 
188.3 

46.60 
41.82 

.0214 
.0239 

151.5 
156.9 

916.5 
912.2 

69.71 
70.18 

986.2 
982.4 

"37-7 
11  39-4 

10 

1440 

.680 

193.2 

37.80 

.0264 

161.9 

908.3 

70.61 

979.0 

1140.9 

11 

1584 

0.748 

197.8 

34.61 

0.0289 

166.5 

904.8 

70.99 

975-8 

1142.3 

12 

1728 

.816 

2O2.O 

31.90 

.0314 

170.7 

901.5 

71-34 

972.8 

ir43-5 

13 

l872 

.884 

205.9 

29-58 

•0338 

174-7 

898.4 

71.68 

970.0 

1144.7 

14 

20l6 

-952 

209.5 

27-59 

.0362 

178.4 

895-4 

72.00 

967.4 

1145-9 

15 

2l6o 

1.020 

213.0 

25-87 

.0387 

181.9 

892.7 

72.29 

965.0 

1146.9 

16 

2304 

1.088 

216.3 

24-33 

0.0411 

l8<.2 

890.1 

72-57 

962.7 

1147.9 

17 

2448 

.156 

219.4 

22.98 

•0435 

188.4 

887.6 

72.82 

960.4 

1148.9 

18 

2592 

.224 

222-4 

21.78 

•0459 

191.4 

885.3 

73-07 

958.3 

1149.8 

J9 

2736 

.292 

225.2 

20.70 

-0483 

T94-3 

883.1 

73-30 

956.3 

1  1  50.6 

20 

2880 

.360 

227.9 

19.72 

.0507 

197.0 

880.9 

73-53 

954-4 

1151.4 

21 

22 

3024 
3l6S 

1.429 

•497 

230.5 
233-0 

18.84 
18.03 

0-0531 
•°554 

199.7 

2O2.  2 

878.8 
876.8 

73-74 
73-94 

952-6 
950.8 

1152.2 
11  53-° 

23 
24 

3312 
3456 

-565 
•633 

235-4 
237-7 

17.3° 
16.62 

.0578 
.0602 

2047 
2O7.O 

874-9 
873-1 

74-13 
74-32 

949.1 
947-4 

"53-7 
"54-4 

25 

3600 

.701 

240.0 

15-99 

.0625 

209.3 

871-3 

74-51 

945-8 

26 

27 
28 

3744 
3888 
4032 

1.769 
•837 
•905 

242.2 

244-3 
246.3 

15.42 
14.88 
14.38 

0.0649 
.0672 
•0695 

2II.5 
213-7 

215-7 

869.6 
867.9 
866.3 

74.69 

74.85 
75-01 

944-3 
942.8 

941-3 

"55-8 
1156.4 

29 

4176 

•973 

248.3 

13.91 

.0619 

217.8 

864.7 

75-:7 

939-9 

llS7-7 

3° 

4320 

2.041 

250.2 

13.48 

.0742 

2I9.7 

863.2 

75-33 

938.5 

"58.3 

31 

32 

4464 
4608 

2.109 
.177 

252.1 
253-9 

12^68 

0.0765 
.0788 

221.6 
223-5 

861.7 
860.3 

75-47 

937-2 
935-9 

1158.8 
1  J  59-4 

33 
34 

4752 
4896 

•245 
•3J3 

255-7 
257-5 

12.32 
11.98 

.0811 
.0835 

225-3 
227.1 

858.9 
857-5 

75-76 
75-89 

934-6 
933-4 

1  1  59.9 
1160.5 

35 

5040 

.381 

259-2 

11.66 

.0858 

228.8 

856.1 

76.02 

932.1 

1161.0 

36 

5184 

2-449 

200.8 

11.36 

0.088  1 

230.5 

854.8 

76.16 

931.0 

1161.5 

P 

39 

40 

5328 
5472 
5616 
576o 

.'585 

•653 

.722 

262.5 
264.0 
265.6 
267.1 

11.07 
10.79 

10-53 
10.29 

-0903 
.0926 
.0949 
.0972 

232.2 
233-8 
235-4 
236.9 

852-3 
851.0 
849.8 

76.28 
76.40 

929.8 
928.7 
927.6 
926.5 

1162.0 
1162.5 
1162.9 
1163.4 

41 

42 
43 
44 
45 

6192 

6336 
6480 

2.789 

•857 
•925 
-993 
3.061 

268.6 
270.1 

271.5 
272.9 

274-3 

10.05 

9-83 
9.61 
9.41 
9.21 

0.0995 
.1018 
.1040 
.1063 
.1086 

238.5 
239-9 
241.4 
242.9 
244.3 

848.7 

847.5 
846.4 
845-2 
844.1 

76.86 
76.97 

77.07 

9254 
924.4 

923-3 
922.3 
921.3 

1163-9 
1164.3 
1164.7 
1165.2 
1165.6 

46 

49 

6624 
6768 
6912 
7056 

3.129 
.197 
-265 
•333 

275.6 
277.0 
278.3 
279.6 

9.02 
8.84 
8.67 
8.50 

.1131 

•1153 
.1176 

245.6 

247.0 

248.3 
249.7 

843.1 

842.0 
841.0 
840.0 

77.29 
77-39 
77-49 
77-58 

920.4 
919.4 
918.5 
9J7-5 

1166.0 
1166.4 
1166.8 
1167.2 

SMITHSONIAN  TABLES. 

238 


TABLE  249. 


PROPERTIES   OF   STEAM. 

British  Measure. 


.ssj-g 

«U 

d 

J 

1     - 

w 

l'|  . 

II 

llc 

li 

S.s  . 

pM    O 

J"  5  s 

Hi 

3   O. 
£   0 

|i 

Ill 

•1*5  1 

2|2 

i  SLIP 

1&P 

~M^ 

J|H 

3  s 

8,7 

S  o  = 

£  E 
fc  « 

g  go 

111 

111 

S  &M 

Ills 

Illri 

Ills 

5  §03 

E?!fl 

50 

52 
53 
54 

7200 

7344 
7488 
7632 
7776 

3.401 
•469 
•537 
.605 

•673 

280.8 
282.1 
283.3 
284-5 
2857 

8-34 
8.19 
8.04 
7.90 
7.76 

0.1198 

.1221 
.1243 
.1266 
.1288 

25I.O 

252.2 
253-5 
254-7 
256.0 

839.0 
838.0 
837-0 
836.0 

77.67 
77.76 
77-85 

77-94 
78.03 

916.6 

915-7 
914.9 
914.0 

9I3-1 

1167.6 

1168^3 
1168.7 

1169.1 

55 

56 

59 

7920 
8064 
8208 
8352 
8496 

'.878 
•946 
4.014 

286.9 
288.1 
289.2 
290.3 
291.4 

7-63 
7-5° 
7-38 
7.26 
7.14 

O.I3IO 
•1333 

•'355 
•1377 

.1400 

257.I 
258.3 
259-5 
260.7 
261.8 

834.2 
833-2 
832.3 
831.5 
830.6 

78.12 
78.21 
78.29 
78.37 
78.45 

912.3 
911.5 
910.6 
909.8 
909.0 

1169.4 
1169.8 
1170.1 

1170.5 

1170.8 

60 

61 
62 
63 

8640 
8784 
8928 
9072 

4.082 
.150 
.218 
.286 

292.5 
293.6 

294-7 
295-7 

7-03 
6.92 
6.82 
6.72 

0.1422 
.1444 
.1466 
.1488 

262.9 
264.0 
265.1 
266.1 

829.7 
828.9 
828.0 
827.2 

78.53 
78.61 
78.68 
78.76 

908.2 

907-5 
906.7 

905-9 

1171.2 

"7I-5 
1171.8 
1172.1 

64 

9216 

•354 

296.7 

6.62 

.1511 

267.2 

826.4 

78.83 

905.2 

1172.4 

65 

66 
67 

/"O 

936o 

9504 
9648 

4.422 
.490 
•558 

297.8 
298.8 
299.8 

6.52 
6.43 
6.34 

0-1533 
•'555 
•1577 

268.3 
269.3 
270.4 

825.6 
824.8 
824.0 

78.90 
78.97 
79.04 

904-5 
903-7 
903.1 

1172.8 
1173.1 

II73-4 

68 
69 

9792 
9936 

.626 
.694 

3OO.I 
301.8 

6.25 
6.17 

-1599 

271.4 
272.4 

823.2 
822.4 

79.11 
79.18 

902.3 
901.6 

"  73-7 
1174.0 

70 

10080 

4.762 

302.7 

6.09 

0.1643 

273-4 

821.6 

79-25 

900.9 

n  74-3 

7l 

10224 

.830 

3037 

6.00 

.1665 

274-3 

820.9 

79-32 

1174.6 

72 

10368 

.898 

304.6 

5-93 

.1687 

275-3 

820.1 

79-39 

899-5 

1174.9 

73 
74 

10512 
10656 

.966 

5-034 

305-5 
306.5 

5.83 
5.78 

.1709 

276.3 

277.2 

819.4 
818.7 

79.46 
79-53 

898.8 
898.1 

H75-1 
"75-4 

75 

76 

77 

10800 
10944 
11088 

5.102 
.170 
.238 

307-4 
308.3 
309-2 

5-70 
5-57 

0.1753 
•1775 
.1797 

278.2 
279.1 
280.0 

817.9 
817.2 
816.5 

79-59 
79-65 
79.71 

897.5 
896.9 
896.2 

"75-7 
1176.0 
1176.2 

78 

11232 

-306 

3IO.I 

5-50 

.1818 

280.9 

815.8 

79-77 

895-6 

1176.5 

79 

11376 

•374 

310.9 

5-43 

.1840 

28l.8 

815.1 

79-83 

895.0 

1176.8 

80 

11520 

5-442 

3II.8 

5-37 

0.1862 

282.7 

814.4 

79-89 

894-3 

1177.0 

81 

11664 

.510 

312.7 

.1884 

283.6 

813.8 

79-95 

893-7 

II77-3 

82 

11808 

.578 

5-25 

.1906 

284.5 

813.0 

80.01 

893-1 

1177.6 

83 

11952 

.646 

3M-4 

.1928 

285.3 

812.4 

80.07 

892.5 

1177.8 

84 

12096 

.714 

3I5-2 

5-*3 

.1949 

286.2 

811.7 

80.13 

891.9 

1178.0 

85 

12240 

5-782 

316.0 

5-°7 

0.1971 

287.0 

811.1 

80.19 

891.3 

1178.3 

86 

11384 

•850 

316.8 

5-02 

•I993 

287.9 

810.4 

80.25 

890.7 

1178.6 

87 

12528 

.918 

317-6 

4.96 

.2015 

288.7 

809.8 

80.30 

890.1 

1178.9 

88 
89 

12672 
12816 

986 
6.054 

318.4 
319.2 

4.91 
4.86 

.2036 
.2058 

289.5 
290.4 

809.2 
808.5 

80.35 
80.40 

889.5 
888.9 

1179.0 
"79-3 

90 

12960 

6.122 

320.0 

4.81 

0.2080 

291.2 

807.9 

80.45 

888.4 

II79-5 

91 

13104 

.190 

320.8 

4-76 

.2102 

292.0 

807.3 

80.50 

887.8 

1179.8 

92     1  13248 

.258 

321.6 

4.71 

.2123 

292.8 

806.7 

80.56 

887.2 

1180.0 

93 

'3392 

•327 

322.4 

4.66 

.2145 

293.6 

806.  1 

80.6  1 

886.7 

1180.3 

94 

13536 

•396 

323-  i 

4.62 

.2166 

294-3 

805.5 

80.66 

886.1 

1180.5 

95 

13680 

6-463 

323-9 

4-57 

0.2188 

295.1 

804.9 

80.71 

885.6 

1180.7 

96 
97 

13824 
13968 

•531 

•599 

324.6 

3254 

4-53 
4-48 

.2209 
.2231 

295-9 
296.7 

804.3 
803.7 

80.76 
80.8  1 

885.0 
884.5 

1180.9 
1181.2 

98 

14112 

.667 

326.1 

4-44 

.2252 

297.4 

803.1 

80.86 

884.0 

1181.4 

99 

14256 

•735 

326.8 

4.40 

.2274 

298.2 

802.5 

80.91 

883.4 

1181.6 

I 

SMITHSONIAN  TABLES. 


239 


TABLE  249, 


PROPERTIES  OF  STEAM 

British  Measure. 


Pressure  in 
pounds  per 
square  inch. 

Pressuie  in 
pounds  per 
square  foot. 

Pressure  in 
atmospheres. 

Temp,  in 
degrees  Fahr. 

ill 

Weight  per 
cubic  foot  in 
pounds. 

Heat  of  water 
Er  pound  in 
T.  U. 

Internal  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

JU    £ 

£  c,  <5,  • 

ins 

Total  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

Total  heat  per 
pound  of  steam  1 
in  B.  T.  U. 

100 

101 

1  02 

14400 

*4544 
!4688 

6.803 
.871 

•939 

327.6 
328.3 
329.0 

4-356 
.316 
.276 

0.2295 
.2317 
.2338 

298.9 
299.7 
300.4 

802.0 
801.4 
800.8 

80.95 

81.00 
81.05 

882.9 
882.4 
881.9 

1181.8 
1182.1 
1182.3 

103 
104 

14832 
14976 

7.007 
-075 

329-7 
330-4 

.237 
.199 

^S? 

301.1 
301.9 

800.3 

799-7 

81.10 
81.14 

881.4 
880.8 

1182.5 
1182.7 

105 

I5I20 

7-T43 

331-1 

4.161 

0.2403 

302.6 

799-2 

81.18 

880.3 

1182.9 

1  06 

15264 

.211 

331-8 

.125 

.2424 

3°3-3 

798.6 

81.23 

879.8 

1183.1 

107 

15408 

.279 

332.5 

.088 

.2446 

304.0 

798.1 

81.27 

879.3 

1183.4 

1  08 
109 

*555| 
15696 

•347 
•4*5 

333-2 
333-8 

•053 
.018 

.2467 
.2489 

304-7 
305-4 

797-5 
797.0 

81.31 
81.36 

878.'3 

1183.6 
1183.8 

110 

in 

112 

15840 

15984 
16128 

7483 
•55* 
.619 

334-5 
335-2 
335-8 

3-984 

•95° 
.917 

0.2510 

•2531 

.2553 

306.1 
306.8 
307-5 

796.5 
795-9 
795-4 

81.41 

81.45 
81.50 

877.9 
877.4 

876.9^ 

1184.0 
1184.2 
1184.4 

i*3 
i*4 

16272 
16416 

.687 

•757 

336.5 
337-2 

.885 
.853 

.2574 

.2596 

308.2 
308.8 

794-9 
794-4 

81.54 
8158 

876.4 
875.9 

1184.6 
1184.8 

115 

16560 

7.823 

337-8 

3.821 

0.2617 

309-5 

793-8 

81.62 

875-5 

1185.0 

116 

16704 

.891 

338.5 

•790 

.2638 

310.2 

793-3 

81.66 

875.0 

1185.2 

117 

16848 

-959 

339-  * 

.760 

.2660 

310.8 

792.8 

81.70 

874-5 

1185.4 

118 

16992 

8.027 

339-7 

•73° 

.2681 

3**-5 

792.3 

81.74 

874.1 

1185.6 

119 

17136 

•095 

340-4 

.700 

.2702 

312.1 

791.8 

81.78 

873.6 

1185.7 

120 

17280 

8.163 

341.0 

3.671 

0.2724 

312.8 

791-3 

81.82 

873-2 

1185.9 

121 
122 

17424 
17568 

.231 
•299 

341.6 
342.2 

•643 
.615 

•2745 
.2766 

3*3-4 

790.8 
790-3 

81.86 
81.90 

872.7 
872.2 

1186.1 
1186.3 

123 

17712 

.367 

342.8 

.587 

.2787 

3*4-7 

789-9 

81.94 

8718 

1186.5 

124 

17856 

•435 

343-5 

.560 

.2809 

3I5-3 

7894 

81.98 

871.4 

1186.7 

125 

18000 

8.503 

344-1 

3-534 

0.2830 

316.0 

788.9 

82.02 

870.9 

1186.9 

126 

18144 

•57* 

344-7 

.2851 

316.6 

788.4 

82.06 

870.5 

1187.1 

127 

18288 

.639 

345-3 

481 

.2872 

317.2 

787-9 

82.09 

870.0 

1187.2 

128 

18432 

.708 

345-9 

-456 

.2893 

317-8 

787-5 

82.13 

869.6 

1187.4 

129 

18576 

.776 

346.5 

•431 

.2915 

318.4 

787.0 

82.17 

869.2 

1187.6 

130 

18720 

8.844 

347-1 

3.406 

0.2936 

319.0 

786.5 

82.21 

868.7 

1187.8 

*3* 

18864 

.912 

347-6 

.382 

•2957 

3*9-7 

786.1 

82.25 

868.3 

1188.0 

132 

19008 

.980 

348.2 

-358 

.2978 

320.3 

785-6 

82.28 

867.9 

1188.1 

19152 

9.048 

348.8 

•334 

.2999 

320.9 

785-1 

82.32 

867.5 

1188.3 

*34 

19296 

.116 

349-4 

.310 

.3021 

32L5 

784.7 

82.35 

867.0 

1188.5 

135 

19440 

9.184 

349-9 

3.287 

0.3042 

322.1 

784.2 

82.38 

866.6 

1188.7 

136 

19584 

.252 

35°-5 

.265 

322.6 

783.8 

82.42 

866.2 

1188.8 

137 

19728 

.320 

351-1 

•424 

'3084 

323-2 

783-3 

82.45 

865.8 

1189.0 

138 
139 

19872 
20016 

.388 
456 

352-2 

.220 
.199 

.3105 

.3126 

323-8 

782.9 
782.4 

82.49 
82.52 

865.4 
865.0 

1189.2 
1189.4 

140 

20160 

9-524 

352-8 

3-177 

0.3147 

325-0 

782.0 

82.56 

864.6 

1189.5 

141 

20304 

.592 

353-3 

.156 

.3168 

325-5 

781.6 

82.59 

864.2 

1189.7 

142 

20448 

.660 

353-9 

.3190 

326.1 

781.1 

82.63 

863.8 

1189.9 

H3 

20592 

.728 

354-4 

•TI5 

.3211 

326.7 

780.7 

82.66 

863.4 

1190.0 

144 

20736 

.796 

355-o 

.094 

.3232 

327-2 

780.3 

82.69 

863.0 

1190.2 

145 

146 

20880 
21024 

9.864 
•932 

355-5 
356-o 

3-074 
•054 

0.3253 

.3274 

327-8 
328.4 

779.8 
779-4 

82.72 
82.75 

862.6 
862.2 

1190.4 
1190.5 

*47 

21168 

10.000 

356.6       .035 

.3295 

328.9 

779-0 

82.79 

861.8 

1190.7 

148 

21312 

.068 

357-1 

.016 

.3316 

778.6 

82.82 

861.4 

1190.9 

149 

21456 

.136 

357-6 

•997 

.3337 

330-0 

778.1 

82.86 

861.0 

1191.0 

SMITHSONIAN  TABLES. 


240 


TABLE  249, 


PROPERTIES  OF  STEAM. 

British  Measure. 


Pressure  in 
pounds  per 
square  inch. 

Pressure  in 
pounds  per 
square  foot. 

Pressure  in 
atmospheres. 

Temp,  in 
degrees  Fahr. 

Volume  per 
pound  in 
cubic  feet. 

iL 

.-IS! 
£il 

Heat  of  water 
per  pound  in 
B.T.U. 

Internal  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

External  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

Total  latent 
heat  per  pound  1 
of  steam  m 
B.  T.  U. 

*3 

ft£»    . 

K1? 

K* 

5  Em 

Sla 

150 

2l6oo 

10.204 

358.2 

2.978 

0-3358 

330-6 

777-7 

82.89 

860.6 

1191.2 

151 

21744 

.272 

358.7 

.960 

•3379 

33I-I 

777-3 

82.92 

860.2 

1191.3 

i$» 

21888 

•340 

359-2 

.941 

•3400 

331-6 

776.9 

82.95 

859-9 

1191.5 

'S3 

i54 

22032 
22176 

.408 
.476 

359-7 
360.2 

•923 
.906 

•3421 
•3442 

332-2 
332-7 

776.5 
776.1 

82.98 
83-01 

859.5 
859.1 

1191.7 
1191.8 

155 

156 

157 
158 

J59 

22320 
22464 
22608 
22752 
22896 

10.544 
.612 
.680 
.748 
.816 

360.7 

361-3 
361.8 

362.3 
362.8 

2.888 
.871 
•854 
•837 
.820 

0.3462 
•3483 
•3504 
•3525 
•3546 

333-2 
333-8 
334-3 
334-8 

335-3 

775-7 
775-3 
774-9 
774-5 
774-1 

83.04 
83-07 
83.10 

83-I3 
83-16 

858.7 

858-3 
858.0 
857.6 
857.2 

1192.0 
1192.1 
1192.3 
1192.4 
1192.6 

160 

161 
162 

'63 
164 

23040 
23184 
23328 
23472 
23616 

10.884 

•952 
II.O2O 
.088 

•157 

363-3 
363-8 
364-3 
364-8 
365-3 

2.803 
•787 
•771 
•755 
•739 

0-3567 

•3630 
•3650 

335-9 
336.4 
336.9 
337-4 
337-9 

773-7 
773-3 
772.9 

772.5 
772.1 

83.19 

83-22 

83-25. 
83.28 

83.31 

856.9 
856.5 
856.1 

855-8 
8554 

1192.7 
1192.9 
1193.0 
1  193.2 

1  1  93-3 

165 

23760 

11.225 

365-7 

2.724 

0.3671 

338.4 

771-7 

83-34 

855-I 

1193.5 

166 
167 

23904 
24048 

•293 
.361 

366.2 
366.7 

•708 
•693 

.3692 
•37.13 

338.9 
339-4 

771-3 
771.0 

83-37 
83-39 

8547 
854-3 

1193.6 
1193.8 

1  68 

24192 

.429 

367.2 

.678 

•3734 

339-9 

770.6 

83.42 

854.0 

11  93-9 

169 

24336 

•497 

3677 

-663 

•3754 

340-4 

770.2 

8345 

853-6 

1194.1 

170 

171 

172 

24480 
24624 
24768 

"•565 
•633 

.701 

368.2 
368.6 
369.1 

2.649 

-634 
.620 

0-3775 
•3796 
•3817 

340.9 
341-4 
341-9 

769.8 
769.4 
769.1 

83.48 
83-5I 
83-54 

853-3 
852.9 
852.6 

1194.2 
1194.4 
IT94-5 

»73 

24912 

.769 

369-6 

.606 

•3838 

342.4 

768.7 

83-56 

8522 

1194.7 

i74 

25056 

.837 

3/0.0 

•592 

.3858 

342.9 

768.3 

83-59 

851.9 

11948 

175 

25200 

11.905 

370.5 

2.578 

0.3879 

343-4 

767.9 

83.62 

851.6 

1194.9 

176 

25344 

•973 

371-0 

•564 

.3900 

343-9 

767.6 

83.64 

851.2 

1195.1 

177 

25488 

12.041 

371-4 

•55° 

.3921 

344-3 

767.2 

83.67 

850.9 

1195.2 

178 

25632 

.109 

371-9 

•537 

•3942 

344-8 

766.8 

83.70 

850-5 

"954 

179 

25776 

.177 

3724 

524 

•3962 

345-3 

766.5 

83-73 

850.2 

II95-5 

180 

25920 

12.245 

372.8 

2.510 

0-3983 

345-8 

766.1 

8375 

849.9 

1195.6 

181 

26064 

•3!3 

373-3 

•497 

.4004 

346.3 

765.8 

8377 

849-5 

1195.8 

182 

26208 

.381 

373-7 

•485 

.4025 

346.7 

7654 

83.80 

849-2 

1  195-9 

183 

26352 

•449 

374-2 

.472 

.4046 

347-2 

765.0 

83-83 

848.9 

1196.1 

184 

26496 

•5'7 

374-6 

•459 

.4066 

347-7 

764-7 

83.86 

848.5 

1196.2 

185 

26640 

12.585 

37  5-  i 

2.447 

0.4087 

348.1 

764-3 

83.88 

848.2 

1196.3 

1  86 

26784 

•653 

375-5 

•434 

.4108 

348.6 

764.0 

83.90 

847.9 

1196.5 

187 

26928 

.721 

376.0 

.422 

.4129 

349-1 

763.6 

83.92 

847.5 

1196.6 

1  88 

27072 

•789 

376.4 

.410 

.4150 

349-5 

763-3 

83-95 

847.2 

1196.7 

189 

27216 

.857 

376.8 

•398 

.4170 

350.0 

762.9 

83.97 

846.9 

1196.9 

190 

27360 

12.925 

377-3 

2.386 

0.4191 

350-4 

762.6 

83.99 

846.6 

1197.0 

191 

275°4 

•993 

377-7 

•374 

.4212 

350.9 

762.2 

84.02 

846-3 

1197.1 

192 

27648 

13.061 

378.2 

.362 

•4233 

35J-3 

761.9 

84.04 

845-9 

ii97-3 

193 

27792 

.129 

378.6 

•35* 

•4254 

351-8 

761.6 

84.06 

845.6 

1197.4 

194 

27936 

.197 

379-o 

•339 

•4275 

352.2 

761.2 

84.08 

845-3 

"97-5 

195 

28080 

13-265 

379-4 

2-328 

0.4296 

352-7 

760.9 

84.10 

845-0 

1197.7 

196 

28224 

•333 

379-9 

•3J7 

.4316 

353-1 

760.5 

84.13 

844.7 

1197.8 

197 

28368 

.401 

380-3 

•306 

•4337 

353-6 

760.2 

84.16 

8444 

1197.9 

198 

28512 

•469 

380.7 

•295 

•4358 

354-0 

759-9 

84.19 

844.0 

1198.1 

199 

28656 

•537 

381.1 

.284 

•4379 

354-4 

759-5 

84.21 

8437 

1198.2 

SMITHSONIAN  TABLES. 


24I 


TABLE  249, 


PROPERTIES  OF  STEAM, 

British  Measure. 


Pressure  in 
pounds  per 
square  inch. 

Pressure  in 
pounds  per 
square  foot. 

il 

1 

l! 

Volume  per 
pound  in 
cubic  feet. 

Weight  per 
cubic  foot  in 
pounds. 

Heat  of  water 
per  pound  in 
B.  T.  U. 

Internal  latent 
heat  per  pound 
of  steam  in 
B  T.  U. 

B*2 

«   3 

•*E,S 

HP 

w|^P5 

Total  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

Total  heat  per 
pound  of  steam  1 
in  B.  T.  U. 

200 

28800 

13605 

381.6 

2.273 

0.4399 

354-9 

759.2 

84.23 

843-4 

1198.3 

201 

28944 

13-673 

382.0 

.262 

.4420 

355-3 

758-9 

84.26 

843.I 

1198.4 

202 

29088 

13-742 

382.4 

.252 

.4441 

355-8 

758.5 

84.28 

842.8 

1198.6 

203 

29232 

13.810 

382.8 

.241 

.4461 

356.2 

758.2 

84.30 

842.5 

1198.7 

2O4 

29376 

13.878 

383.2 

.231 

.4482 

356-6 

757.9 

84.33 

842.2 

1198.8 

205 

29520 

13.946 

383.7 

2.221 

0.4503 

357-1 

757.5 

84.35 

841.9 

1199.0 

206 

29664 

14.014 

384.1 

.211 

•4523 

357-5 

757-2 

84.37 

841.6 

1199.1 

207 

29808 

14.082 

384-5 

.201 

-4544 

357-9 

84.40 

841.3 

1199.2 

208 
209 

29952 
30096 

14.150 
14.218 

384-9 
385.3 

.191 

.4564 
.4585 

358-3 

756-6 
756.2 

84.42 
8444 

841.0 
840.7 

"99-3 
1199.4 

210 

211 

30240 
30384 

14.386 
14-454 

3^1 

2.I7I 
.162 

0.4605 
.4626 

359-2 
359-6 

755-9 
755-6 

84.46 
84.48 

840.4 
840.1 

1199.6 
1  199.7 

212 

30528 

14.522 

386.5 

.152 

.4646 

360.0 

755-3 

84.51 

839.8 

1199.8 

2I3 
214 

30672 
30816 

14.590 
14.658 

386.9 
387.3 

•143 
•134 

.4666 
.4687 

360.4 
360.9 

755-o 
754-7 

84.53 
84.55 

839-5 
839-2 

1199.9 

1200.1 

215 

216 
217 

30960 
31104 
31248 

14.726 
14.794 
14.862 

387-7 
388.1 
388.5 

2.124 

0.4707 

.4727 
.4748 

361.3 
361-7 
362.1 

754-3 
754-0 
753-7 

84.57 
84.60 
84.62 

838.9 
838.6 
838.3 

1200.2 
I2OO.3 
I  200-4 

218 
219 

31536 

14.930 
14.998 

388.9 
389-3 

& 

.4768 
.4788 

362.5 
362.9 

753-4 
753-1 

84.64 
84-66 

838.0 
8377 

1200-5 
I2OO-7 

SMITHSONIAN  TABLES. 


242 


TABLE  250. 


RATIO  OF  THE   ELECTROSTATIC  TO  THE  ELECTROMAGNETIC  UNIT  OF 
ELECTRICITY  (v)  IN   RELATION  TO  THE  VELOCITY  OF  LIGHT. 


Ratio  of  electrical  units. 

Reference. 

Date  of 
determina- 
tion. 

V 

in  cms.  per  sec.* 

Determined  by  — 

Publication. 

Year. 

1856 

3.107  X  io10 

Weber  &  Kohlrausch  . 

Pogg.  Ann. 

1856 

1868 

2.842  X  io10 

Maxwell 

Phil.  Trans.     . 

1868 

1869 

2.808  X  io10 

W.  Thomson  &  King  . 

B.  A.  Report  . 

1869 

1872 

2.896  X  io10 

McKichan     . 

Phil.  Trans.     . 

1872 

1879 

2.960  X  101° 

Ayrton  &  Perry    . 

Jour.  Soc.  Tel.  Eng. 

1879 

1879 

2.968  X  io10 

Hocken 

B.  A.  Report  . 

1879 

1880 

2.955  X  io10 

Shida    .        .        .        . 

Phil.  Mag.       . 

1880 

1881 

2.99   Xio10t 

Stoletow       ,       .       . 

Soc.  de  Phys.  . 

1881 

1881 

3.019  X  io10 

Klemencic     . 

Wien.  Ber.      . 

1884 

1882 

2.923  X  io10 

Exner    .        .        . 

Wien.  Ber.       . 

1882 

1883 

2.963  X  io10 

J.  J.  Thomson 

Phil.  Trans.     . 

1883 

1888 

3.009  X  io10 

Himstedt       . 

Wied.  Ann.  35 

1888 

1889 

2.981  X  io10 

Rowland        .        .        . 

Phil.  Mag. 

1889 

1889 

3.000  X  io10 

Rosa      . 

«       « 

1889 

1889 

3.004  X  io10 

W.  Thomson 

Phil.  Mag. 

1889 

1890 

2.995  X  io10 

J.  J.  Thomson  &  Searle 

Phil.  Trans.      . 

1890 

*  The  results  in  this  column  correspond  to  a  value  of  the  B.  A.  ohm  =  .98664  X  io9  cms.  per  sec.  If  we  neglect 
the  first  four  determinations,  and  also  that  of  Exner  and  Shida,  because  of  their  large  deviation  from  the  mean,  the 
remaining  determinations  give  a  mean  value  of  2.9889  +  .0137,  a  value  which  practically  agrees  with  the  best  deter- 
minatiors  of  the  velocity  of  light.  (Cf.  Table  181.) 

t  Given  as  between  2.98  X  io10  and  3.00  X  io10. 

SMITHSONIAN  TABLES. 

243 


TABLE  251 . 


DIELECTRIC   STRENGTH. 

Difference  of  Electric  Potential  required  to  produce  a  Spark  in  Air. 


(a)  MEDIUM,  AIR.     ELECTRODE  TERMINALS,  FLAT  PLATES. 


Spark  length 

in 
centimetres. 


O.OI 
O.O2 
0.04 
0.07 
0.10 
O.I4 
O.2O 
0.30 
0.40 
0.50 
O.6O 
0.80 
1. 00 


Difference  of  potential  in  volts  required  to  produce  a  spark  according  to  — 


W.  Thomson.1      De  la  Rue.2        MacFarlane.3  Bailie.* 


790 
1340 
1840 
2940 
4010 

53°° 


500 

970 

1900 

3170 

4330 

5740 

7620 

10400 


3507 

S7i5 

7818 

9879 

11925 

13956 
18006 
22044 


4401 

7653 
10603 

I343I 
16341 
19146 
25458 
3^47 


Freyberg.* 


4344 

7539 
10671 
13665 
16293 

19059 
24465 
28800 


1  "  Reprint  of  Papers  on  Elect,  and  Mag."  p.  252.     2  "  Proc.  R.  Soc."  vol.  36,  p.  151. 

3  "  Phil.  Mag."  vol.  10,  1880.  4  "  Ann.  de  Chim.  etde  Phys."  vol.  25,  1882. 

5  «<  Wied.  Ann."  vol.  38,  1889. 


(b)  MEDIUM,  AIR.     ELECTRODE  TERMINALS,  BALLS  OF  DIAMETER  d  IN  CENTIMETRES. 


Experiments  of  Freyberg. 


Spark  length 

in 
centimetres. 


d  —  o  (points). 


d  —  o.  50 


d—  i.o 


d  —  4.0 


=  6.o 


O.I 

0.2 

o-3 

0.4 

0.6 
0.8 

I.O 
2.O 

5-° 


3720 
4700 

53°° 
6000 
6900 
8100 
8600 

IOIOO 

13100 


moo 


16600 
18400 

19500 

24600 

30700 


4660 
9500 

11700 
14000 

19300 

23200 
25800 
35400 


4560 

8700 

11600 

14400 

19500 

24600 
29000 


8400 

1 1 200 

I42OO 
2CIOO 
25800 
29900 


4530 
7900 
I050O 
I280O 
I92OO 
26OOO 
31600 


From  the  above  table  it  appears,  as  remarked  by  Freyberg,  that  for  each  length  of  spark  there  is  a  par- 
ticular size  of  ball  which  requires  the  greatest  difference  of  potential  to  produce  the  spark. 


(o)  COMPARISON  OF  RESULTS  OF  DETERMINATIONS,  THE  TERMINALS  BEING  BALLS. 


Spark 
length 
in  cms. 


•9 

I.O 


Difference  of  potential  required  to  produce  a  spark  in  air  according  to  — 


Bailie.      gjJSgJ    Paschen. 


Balls  i  centimetre  diameter. 


4590 
8040 
11190 
13650 
16410 
19560 
21690 
23280 
24030 
24930 


42OO 
8130 
I0860 
14130 
16800 
19350 
21030 
23190 
24540 
25800 


4860 
8430 
11670 
14830 
17760 
20460 
22640 
24780 


4660 
9500 
11670 
13980 
16800 
19260 
20970 
23220 
25110 
25770 


Paschen.     Freyberg.    Quincke. 


Balls  2  cms.  diameter. 


4830 
8340 
11670 
14820 
18030 
20820 
23670 


4560 
8700 

11 55° 
14400 
17040 
19470 
22530 
24630 
27240 
29040 


4440 
7920 
1 1190 
14010 
16920 
19980 
22590 
25770 


Bailie.       Freybei 


Balls  6  cms.  diam. 


4440 
7680 
10830 
13500 
IOS30 
19560 
22620 
26400 
29220 
33870 


4530 
7860 
10470 
12750 
16410 
19200 
22590 
26010 
28770 
31620 


"  Electricien,"  Aug. 


Wied.  Ann."  vol.  19,  1883. 


SMITHSONIAN  TABLES. 


TABLES  252,  253. 
DIELECTRIC    STRENGTH. 

TABLE  252.  —Effect  of  Pressure  of  the  Gas  on  the  Dielectric  Strength.* 

Length  of  spark  is  indicated  by  I  in  centimetres.     The  pressure  is  in  centimetres  of  mercury  at  o°  C. 


Hydrogen. 

Air. 

Carbon  dioxide. 

7  =  0.2 

7=0.4 

7=o.6 

7=0.2 

,=  o.4 

7=o.6 

7=0.2 

7=o.4 

7=o.6 

2 

510 

606 

819 

I2O2 

1536 

II25 

1446 

1650 

4 

729 

1017 

1437 

1140 

1725 

2289 

1431 

K 

^71 

2373 

6 

945 

1323 

ifc 

39 

1455 

2229 

3OI2 

:755 

2i 

&4 

3I05 

8 

1098 

I 

572 

2172 

1740 

2721 

3684 

2070 

2913 

3813 

10 

1242 

] 

806 

2463 

2004 

3l86 

4272 

2355 

3- 

288 

4278 

15 

1584 

2376 

3330 

2664 

4212 

5736 

2991 

4227 

5592 

20 

25 

1866 
2169 

2937 
3444 

4020 
4668 

3294 
38l6 

$% 

7074 
8346 

3705 
4248 

5235 
6120 

6801 
8004 

3° 

2475 

3957 

533  i 

4347 

7020 

9570 

4707 

6921 

9T47 

35 

2748 

4407 

5997 

4845 

7980 

10797 

5163 

7737 

10293 

40 

3051 

4863 

6681 

5349 

8853 

12009 

5772 

8543 

"397 

45 

3339 

5 

334 

7347 

5853 

9639 

13224 

6222 

93°3 

12483 

5° 

3606 

5 

829 

7971 

6288 

I043I 

14361 

6489 

10038 

X3557 

H 

2834 
4107 

6294 
6747 

8583 
9222 

6711 
7134 

II259 
12084 

I544I 
16548 

6789 
7197 

10650 
"397 

14610 

15702 

65 

4476 

7197 

9867 

7569 

12885 

17688 

7605 

12114 

16740 

70 

473  i 

7629 

10476 

8016 

I37IO 

18804 

8001 

12816 

17727 

75 

4914 

8031 

11040 

8487 

19896 

8388 

13506 

18705 

Paschen  deduces  from  the  above,  and  also  shows  by  separate  experiments,  that  if  the  product  of  the  pressure 
of  the  gas  and  the  length  of  spark  be  kept  constant  the  difference  of  potential  required  to  produce  the  spark 
also  remains  constant. 

In  the  following  short  table  I  is  length  of  spark,  P  pressure,  and  ^difference  of  potential,  the  unit  being 
the  same  as  above.     The  table  illustrates  the  potential  difference  required  to  produce  a  spark  for  different 
values  of  t!  e  product  l.P. 

l.P. 

FforH 

V  for  Air. 

V  for  CO2             l.P. 

Ffor  H 

V  for  Air. 

V  for  C02 

O.2 

f- 

669 

873               6.0 

2481 

4251 

4443 

0.4 

837 

IIIO                  IO.O 

3507 

6l62 

6198 

0.6 

996 

I28l                   2O.O 

5835 

10392 

1  001  1 

I.O 

846 

1326 

1599                  30.0 

13448 

r3527 

2.O 

1427 

2019 

2271                   45.0 

IIOI3 

19848 

18705 

4.0 

1884 

3216 

3468 

TABLE  253.  —  Dielectric  Strength  (or  Difference  of  Potential  per  Centimetre  of  Spark  Length)  of  Different 

Substances,  in  Kilo  Volts,  t 


Substance. 

C  1* 

Substance. 

5  w 

Substance. 

11 

3* 

Q  " 

jgi 

8' 

Air  (thickness  5  mm.) 
Carbon  dioxide     "       .     . 

23.8 
22.7 

Beeswaxed  paper     . 
Paraffined  paper 

540. 
360. 

Kerosene  oil  .     .     . 
Oil  of  turpentine     . 

94- 

Coal  gas                 "       .     . 
Hydrogen              "       .     . 
Oxygen                   "       .     . 

22.2 
22.3 

Paraffin  (solid)    .     . 

Olive  oil      .... 
Paraffin  oil      ... 
Paraffin  (melted)      . 

82. 
87. 
56. 

SMITHSONIAN  TABLES. 


*  Paschen. 

t  MacFarlane  and  Pierce,  "  Phys.  Rev."  vol.  i,  p.  165,  1893. 

245 


TABLE  254. 
COMPOSITION    AND    ELECTROMOTIVE    FORCE    OF    BATTERY   CELLS. 

The  electromotive  forces  given  in  this  table  approximately  represent  what  may  be  expected  from  a  cell  in  good  work- 
ing order,  but  with  the  exception  of  the  standard  cells  all  of  them  are  subject  to  considerable  variation. 


(a)  DOUBLE  FLUID  BATTERIES. 

Name  of 
cell. 

Negative  pole. 

Solution. 

Positive 
pole. 

Solution. 

fe£ 

Sg 

w.s 

Cunsen  .     . 

Amalgamated  zinc 

(  i  part  H2SO4  to  T 
\     12  parts  H2O  .  f 

Carbon 

Fuming  H2NOg 

1.94 

« 

«                « 

« 

u 

HNO3,  density  1.38 

1.86 

Chromate  . 

«                « 

f  i2partsK2Cr2O7l 
to  25  parts  of  1 
H2SO4  and  100  f 
[    parts  H2O  .     .  J 

« 

(  i   part   H2SO4  to  \ 
I      12  parts  H2O     .  f 

2.00 

« 

«                « 

(  i  part  H2SO4  to  ( 
(      12  parts  H2O  .  j 

«( 

(  12  parts  K2Cr2O7  ^ 
(    to  loo  parts  H2O  j 

2.03 

Daniell*   . 

«                « 

(  i  part  H2SO4  to  ) 
(      4  parts  H2O    .  J 

Copper 

j  Saturated  solution  ) 
I  ofCuSO4+sH2O  J 

1.  06 

« 

«                « 

(  i  part  H2SO4  to  ) 
(      1  2  parts  H2O  .  ] 

<« 

M 

1.09 

« 

4<                             « 

(  5%    solution    of  [ 
\    ZnS04  +  6H20( 

tt 

«< 

1.08 

« 

<«                   «( 

(  i   part  NaCl   to  ) 
(      4  parts  H2O   .  ) 

tt 

II 

1.05 

Grove   .     . 

«                   «( 

(  i  part  H2SO4  to  ) 
(      12  parts  H2O  .  j 

Platinum 

Fuming  HN03  .    . 

i-93 

.     . 

((                       « 

Solution  of  ZnSO4 

« 

HNO3,  density  1.33 

1.66 

« 

«<                       « 

(  H2SO4  solution,  ) 
\      density  1.136  .  J 

«« 

Concentrated  HNO3 

i-93 

« 

<<                   « 

(  H2SO4  solution,  ) 
(      density  1.136  .  } 

u 

HNO3,  density  1.33 

1.79 

tt 

i«                       <( 

(  H2SO4  solution,  ) 
(      density  1.06     .  J 

« 

« 

1.71 

« 

<(                       « 

(  H2SO4  solution,  ) 
(      density  1.14    .  J 

it 

HNO3,  density  1.19 

1.66 

« 

«                  (( 

(  H2SO4  solution,  ) 
|      density  1.06     .  ) 

« 

U                   ((                     « 

1.61 

« 

«(                       «< 

NaCl  solution  .    . 

« 

"       density  1.33 

1.88 

Marie  Davy 

«                   <( 

(  i  part  H2SO4  to  ) 
(      12  parts  H2O    J 

Carbon 

(  Paste  of  protosul-  ) 
<    phate  of  mercury  > 
(    and  water  .     .     .  ) 

1.50 

Partz     .    . 

«                       « 

Solution  of  MgSO4 

« 

Solution  of  K2Cr2O7 

2.06 

*  The  Minotto  or  Sawdust,  the  Meidinger,  the  Callaud,  and  the  Lockwood  cells  are  modifications  of  the  Daniell, 
ana  hence  have  about  the  same  electromotive  force. 

SMITHSONIAN  TABLES. 

246 


TABLE  254, 
COMPOSITION    AND    ELECTROMOTIVE    FORCE    OF    BATTERY   CELLS. 


Name  of  cell. 

Negative 
pole. 

Solution. 

Positive  pole. 

j  

E.  M.  F. 

in  volts. 

(V)  SINGLE  FLUID  BATTERIES. 

f  Carbon  surround-  ) 

Leclanche    .    .     . 

Amal.  zinc 

(  Solution  of  sal-ammo-  ) 
(      niac  J 

1  ed  by  powdered 
I  carbon  and  perox-  f 

I.46 

[  ide  of  manganese  J 

Chaperon     .     .     . 

« 

(  Solution  of  caustic       | 
|      potash  j 

Copper  and  CuO 

0.98 

Edison-Lelande    . 

« 

" 

« 

0.70 

Chloride  of  silver 

Zinc    .    . 

23  %  solution  of  sal-    ) 
ammoniac   .     .     .      ) 

(  Silver  surrounded  ) 
|    by  silver  chloride  J 

I.  O2 

Law     

u 

15%           "             " 

Carbon 

_     _  — 

(i  pt.  ZnO,  i  pt.  NH4C1,  ] 

•J7 

Dry  cell  (Gassner 

« 

3  pts.  plaster  of  paris,  ! 
2  pts.ZnCl2,  and  water  j 

« 

I.3    • 

to  make  a  paste     .     .  J 

Poggendorff     .     . 

Amal.  zinc 

\  Solution  of  chromate 
)      of  potash    .... 

« 

1.  08 

(  12  parts  K2Cr2O7  -f-    ) 

" 

« 

25  parts  H2S04  +    [ 

u 

2.01 

(      100  parts  H2O    .     .  ) 

I  i  part  H2S04  +            ) 

J.  Regnault  .     .     . 

u 

I      1  2  parts  H2O  +        > 

Cadmium    .    .     . 

034 

(      i  part  CaSO4      .     .  ) 

Volta  couple     .     . 

Zinc    .     . 

H20      ... 

Copper   .... 

0.98 

(o)  STANDARD  CELLS. 

Kelvin,  Gravity,  ) 
Daniell  .    .     .  J 

Amal.  zinc 

(  ZnSO4  solution,  den-    } 
\      sity  1.40      .     .     .     .  J 

f  Mercurous  sulphate  in  | 

(  Electrolytic  cop-     ) 
1  per  in  CuSO4sol.  > 
(  density  i.io    .    .  ) 

(  1.072  [I 
<  —  .OOOl6 
((^-15)] 

Clark  standard  . 

M 

paste  with  saturated  I 
solution   of    neutral  f 

Mercury.    .    .    . 

(  r-434  t1 
j  —.00077 

[     ZnSO4  j 

(  (t    J5)J 

f  0.50  tem- 

Bailie &  Ferry   . 

« 

(  Zinc  chloride,  density   | 

1        T  i  (-7                                    ( 

(  Lead  surrounded  ) 
I   by  powdered         > 
1    PbCl2    .    .    .    .) 

perature 
•{  coeffic't 
j  about 

1  .0001  1 

C  Oxide  of  mercury  in  a  ^ 

(  I-387  [i 

Gouy     .... 

" 

10  %  sol.  of  ZnSO4  > 

Mercury.     .     .    . 

j  —  .0002 

(      (paste)   ) 

(  (f—  12)] 

Lodge's  standard  cell  and  Fleming's  standard  cell  are,  like  the  Kelvin  cell  above,  modifications  of  the  Dan- 
iell zinc-zinc  sulphate,  copper-copper  sulphate  cell. 

(d)  SECONDARY  CELLS. 

Faure-Sellon-        ) 
(Volckmar)     .  J 

Lead    .    . 

j  H2SO4  solution  of         ) 
1      density  i.i       .     .     .  f 

pbO2  

2.2* 

(  1.68  to 

Regnier  (i)    .     . 

Copper    . 

CuSO4+H2SO4  .    . 

"       

<  0.85,   av- 

(  erage  1.3. 

(2)     .      . 

Amal.  zinc 

ZnSO4  solution  .     .     . 

"      in  H2SO4     .     . 

2.36 

Main      .... 

Amal.  zinc 

H2SO4densityab'ti.i 

14 

2.50 

F.  Streintz  gives  the  following  value  of  the  temperature  variation  — -  at  different  degrees  of  charge 


E.  M.  F. 

dE/dtXio* 

E.  M.  F. 

dEfdtXio* 

E.  M.  F. 

dEfdtX  io« 

1.9223 
1.9828 

140 
228 

2.0031 
2.0084 
2.0105 

335 
285 

255 

2.0779 
2.2070 

130 

73 

SMITHSONIAN  TABLES. 


247 


TABLE  255, 


THERMOELECTRIC  POWER. 


The  thermoelectric  power  of  a  circuit  of  ^"J^™ 

for  one  degree  difference^  of  tempera  ure     e   ^  _  ._t  ~_  t  — „„„,„,.„  ot  which  the  thermoelectric  power  vanishes. 


jr.  i  jf  — j,  /  — A  / g  and  tins  tne  neuirai  pumi  <->i  tcm[jcjamit  «»i  "»i»x.».  »•.«-  >..~; r--  —   •  •--- 

£?  7  • —  r  ti,  _:«,,  v>pot  nf  electricitv  to  the  absolute  value  of  the  temperature  t  is  expressed  by  — a  tor  any 
^^^l2^^^2T^S^^k  power  of  different  couples  may  be  inferred  from  the 
^hlefsti  the  difference  of  the  tabulated  values  with  respect  to  lead,  which  is  here  taken  as  zero.  The  table, 
fas  been  compiled  romThe  results  of  Becquerel,  Matthieson,  and  Tait.  In  reducing  the  results  the  electromotive 
force  of  the  Grove's  and  the  Daniell  cells  have  been  taken  as  1.95  and  1.07  volts  respectively. 


Thermoelectric  power 

Neutral 

Substance. 

A 

B  X  jo-3 

at  mean  temp,  or 
junctions  (microvolts). 

point 
A 

Author- 
ity. 

20°  C. 

50°  C. 

B 

Aluminium          .         .        •     .  ' 
Antimony,  comm'l  pressed  wire 
"          axial 

0.76 

—0.39 

0.68 

—6.0 

—22.6 

0.56 

195 

T 
M 

"          equatorial 

- 

- 

—  26.4 

- 

- 

it 

"          ordinary   . 
Argentan    

11.94 

5.06 

—17.0 
12-95 

14.47 
12.7 

-236 

T 
B 

Arsenic       

- 

- 

I3-56 

- 

M 

Bismuth,  comm'l  pressed  wire  . 

- 

- 

97-0 

- 

— 

"        pure            "          "     • 

— 

- 

89.0 

~ 

~ 

"         crystal,  axial 

— 

- 

65.0 

— 

— 

"             "       equatorial 
"        commercial 

: 

: 

45-o 

39-9 

*™ 

B 

—2.63 

—  4.24 

—348 

—  4-  7  5 

—62 

T 

"        fused  .... 

3 

—2-45 

- 

B 

Cobalt        

- 

- 

22. 

- 

M 

—  1-34 

—  0.94 

—  1.52 

—  1.81 

—  H3 

T 

"       commercial    . 

Of 

—  O.IO 

- 

M 

"       galvanoplastic 

- 

- 

-3-8 

- 

- 

" 

Gold           

— 

— 

—  1.2 

— 

— 

—2.80 

—  I.OI 

3-O 

—  3-3° 

—277 

T 

Iron    

—  17>1S 

4.82 

-16.2 

—14.74- 

356 

u 

"     pianoforte  wire  . 

- 

—17-5 

- 

M 

"     commercial 

— 

— 

— 

—  12.  IO 

— 

B 

"             " 

- 

— 

— 

9-10 

— 

" 

Lead                '             ... 

_ 

o.oo 

o.oo 

O.OO 

_ 

_ 

Magnesium         .... 

—  2.22 

0.94 

—2.03 

—1-75 

236 

T 

Mercury     

— 

— 

0.413 

— 

- 

M 

"            ..... 

— 

— 

— 

3-3° 

— 

B 

Nickel        

— 

— 

— 

i   1S-S° 

— 

" 

"       (—18°  to  175°)       . 

21.8 

5.06 

22.8 

M          "^     « 

24-33 

-438 

T 

"       (25o°-3oo°)     .        .'       . 

83-57 

-23.84 

- 

- 

" 

"       (above  340°)  . 

3-°4 

5.06 

— 

— 

— 

" 

Palladium  

6.18 

3-55 

6.9 

7-96 

—174 

" 

•   "         ". 

— 

6.9 

— 

B 

Phosphorus  (red) 

- 

- 

—29.9 

- 

M 

Platinum     

— 

— 

—0-9 

— 

— 

" 

"         (hardened) 

—2.5? 

0.74 

—2.42 

—  2.  2O 

347 

T 

(malleable)  . 

0.60 

1.09 

8.82 

J.IS 

—55 

" 

"        wire     .... 

— 

— 

- 

—0.94 

— 

B 

"         another  specimen 

— 

— 

— 

2.14 

— 

" 

Platinum-iridium  alloys  : 

85%Pt  +  is%Ir 

—7.90 

—  0.62 

—8.03 

—8.21 

—1274 

T 

9o%Pt  +  io%Ir 
95%Pt+    5%Ir      .    ..       v 

-5.90 
—  6.15 

i-33 

—  °-55 

33 

—5-23 
—  6.42 

444 
—  1118 

u 
ft 

Selenium    ..... 

— 

-807. 

— 

— 

M 

Silver          .         .         ..',.-.- 

—  2.12 

—1.47 

—2.41 

—2.86 

—144 

T 

"       (pure  hard) 

- 

—3.00 

- 

M 

"       wire                           , 

_ 

_ 

—2.18 

_ 

B 

Steel  

—11.27 

3-25 

—  10.62 

—9-65 

347 

T 

—  W. 

M 

_ 

_ 

ow-« 

—429.3 

_ 

B 

Tin  (commercial) 

- 

- 

- 

—0-33 

- 

" 

"...... 

_ 

_ 

—  O.I 

_ 

M 

"        

°-43 

—0.^5 

°-33 

0.16 

78 

T 

Zinc             ..... 

-2.32 

-2.38 

—2-79 

—  3-51 

-98 

" 

"     pure  pressed 

-3-7 

- 

M 

B  =  Ed.  Becqnerel,  "  Ann.  rle  Chim.  et  de  Phys  "  [4]  vol   8.              M  =  Matthieson,  "  Po«rp.  Ann."  vol.  103, 

T  =  Tait,  "Trans.  R.  S.  E."  vol.  27,  reduced  by  Mascart.                                reduced  by  Fleming  Jenkin. 

SMITHSONIAN  TABLES. 


'2  AS 


TABLE    256. 


THERMOELECTRIC    POWER    OF   ALLOYS. 


The  thermoelectric  powers  of  a  number  of  alloys  are  given  in  this  table,  the  authority  being  Ed.  Becquerel.  They  are 
relative  to  lead,  and  for  a  mean  temperature  of  50°  C.  In  reduciug  the  results  from  copper  as  a  reference  metal, 
the  thermoelectric  power  of  lead  to  copper  was  taken  as  — 1.9. 


Substance. 

Relative 
quantity. 

Thermo- 
electric 

power  in 
microvolts. 

Substance. 

Relative 
quantity. 

Thermo- 
electric 
power  in 
microvolts. 

Antimony   . 
Cadmium    . 

806 
696 

1 

227 

Antimony   . 
Bismuth      .         . 

'?! 

8.8 

Antimony   . 

4 

Antimony   . 

4l 

Cadmium    . 

2< 

146 

Iron     .... 

ij 

2-5 

Zinc    .... 

I 

i 

Antimony   . 

8i 

Antimony   . 

806) 

Magnesium 

if 

1.4 

Cadmium    . 
Bismuth 

696  [ 
121) 

137 

Antimony    . 
Lead   .... 

11 

—0.4 

Antimony   . 

806 

f\  p 

Bismuth      .         . 

-43-8 

Zinc    .... 

406  j 

95 

Bismuth 

2  I 

Antimony   . 

806; 

Antimony   . 

M 

—33-4 

Zinc    .... 

406  1 

8.1 

Bismuth 

4i 

Bismuth      . 

121  ! 

> 

Antimony   . 

if 

'      5M 

Antimony  .         . 
Cadmium    . 

4' 

2 

Bismuth 
Antimony   . 

?! 

—  63.2 

Lead  .... 

I 

70 

Bismuth 

10  I 

Zinc    . 

I 

Antimony   . 

I  f 

—  68.2 

Antimony  . 
Cadmium    . 

2 

.£. 

Bismuth 
Antimony    . 

"1 

—66.9 

Zinc    .... 

I 

40 

Bismuth 

2  [ 

Tin      . 

I 

Tin     .          . 

••1 

60 

Antimony   . 
Zinc    .... 

T< 

A    1 

43 

Bismuth 
Selenium     . 

"I 

—24-5 

Tin      .... 

j    ' 

Bismuth 

12) 

Antimony   . 

12  j 

Zinc   .... 

if 

—  31-1 

Cadmium    . 
Zinc    .... 

l! 

35 

Bismuth 
Arsenic 

"| 

—  46.0 

Antimony   . 
Tellurium    . 

10 

i 

10.2 

Bismuth 
Bismuth  sulphide  .     . 

1} 

68.1 

TABLE  257. 
NEUTRAL  POINTS  WITH   LEAD.* 


Substance. 

Temp. 

Substance. 

Temp. 

Bismuth  . 

—580° 

Zinc  .     .     . 

-95° 

Nickel     . 

—424 

Cadmium  . 

—59 

Gold    .     . 

-276 

Platinum    . 

-56 

Argentan 

-238 

Tin    .     .     . 

75 

Cobalt      . 

—228 

Rhodium    . 

132 

Palladium 

—172 

Ruthenium 

136 

Antimony 

-156 

Aluminium 

212 

Silver  . 

—144 

Magnesium 

239 

Copper    . 

—132 

Iron  .     .     . 

356 

TABLE   258. 
SPECIFIC    HEATS    OF    ELECTRICITY.! 

The    numbers    are    the    coefficients   B    in    the    equation 

—  =.A+Bt,  and  have  to  be  multiplied  by  the  absolute 

tU 

temperature  T  to  give  the  specific  heat  of  electricity.     (See 

also  Table  255.) 


Metal. 

Sp.ht.  of  el. 

Metal. 

Sp.  ht.  of  el. 

T 

T 

Alumin- 

Magnesium 

—.00094 

ium  .     . 

.00039 

Nickel  : 

Antimony 

.O222I 

To  175°  C.  . 

—.00507 

Argentan 

—.00507 

25o°-3io°     . 

.00219 

Bismuth  . 

—.01073 

Above  340°  . 

—•00351 

Cadmium 

.00425 

Platinum  (soft) 

—  .00109 

Cobalt      . 

—  .01141 

Palladium    . 

—-00355 

Copper     . 

.00094 

Rhodium     .     . 

—.00113 

Gold    .     . 

.OOIOI 

Rubidium    .     . 

—  .00206 

Iron 

—  .00481 

Silver      .     .     . 

.00148 

Indium    . 

.00000 

Tin      .... 

.00055 

Lead    .     . 

.00000 

Zinc    .... 

.00235 

*Tait's  "  Heat,"  p.  180. 

t  Calculated  from  a  table  given  by  Tait  by  assuming  che  electromotive  force  of  a  Grove  s  cell  —  1.95 

SMITHSONIAN  TABLES. 

249 


volts. 


TABLE  259. 

THERMOELECTRIC    POWER   OF    METALS   AND   SOLUTIONS.* 

Thermoelectric  power  of  circuits,  the  two  parts  of  which  are  either  a  metal  and  a  solution  of  a  salt  of  that  metal  or 
two  solutions  of  salts.  The  concentration  of  the  solution  was  such  that  in  1000  parts  of  the  solution  there  was 
one  half  gramme  equivalent  of  the  crystallized  salt.  The  circuit  is  indicated  symbolically ;  for  example,  Cu  and 
CuSO4  indicates  that  the  circuit  was  partly  copper  and  partly  a  solution  of  copper  sulphate. 


Thermoelec- 

Substances forming  circuit. 

tric  power  in 

Insoluble  salts  mixed  with  a  solution  of 

the    corresponding   zinc    or   cadmium  salts 

for  the  purpose  of  acting  as  a  conductor. 

Cu  and  CuSO4    

754 

The  other  part  of  the  circuit  was  the  metal 

Zn  and  ZnSO4 
Cu  and  CuAc  (acetate) 
Pb  and  PbAc       . 

760 
660 
176 

of  the  insoluble  salts.     The  results  are  com- 
plex and  of  doubtful  value. 

Zn  and  ZnAc 

693 

Cd  and  CdAc 

5°3 

Zn  and  ZnCl2 
CdandCdCl2      . 
Zn  and  ZnBr2      . 

5fc 
$ 

Substances  forming  circuit. 

Thermoelectric 
power  in 
microvolts. 

Zn  and  ZnI2 

OO2 

CdandCdI2 

594 

Ag  and  AgCl  in  ZnCJ2 

143 

Ag  and  AgCl  in  CdCl2 

310 

CuSO4  and  ZnSO4      . 

40 

Ag  and  AgBr  in  ZnBr2 

CuAc  and  ZnAc  . 
ZnAc  and  CdAc  . 

8 
o 

Ag  and  AgBr  in  CdBr2 
Ag  and  Agl  in  ZnI2 

461 
414 

CuAc  and  CdAc  . 

0 

Ag  and  Agl  in  CdI2     . 

unsuccessful 

PbAc  and  ZnAc  . 

73 

Hg  and  Hg2Cl2  in  ZnCl2     . 

680 

PbAc  and  CdAc  . 
PbAc  and  CuAc  . 
ZnCl2  and  CdCl2 

54 
133 
9 

Hg  and  Hg2Cl2  in  CdCl2     . 
Hg  and  Hg2Br2  in  ZnBr2     . 
Hg  and  Hg2Br2  in  CdBr2     . 

673 
650 

ZnBr2  and  CdBr2 
ZnI2  and  CdI2     . 

U 

Hg  and  Hg2I2  in  ZnI2  . 
Hg  and  Hg2I2  in  CdI2         .  "1 

^ 

TABLES  26O,  261. 

PELTIER    EFFECT. 

TABLE  260.  -  Jain's  Experiments. t  TABLE  261.  -Le  Rome's  Experiments. $ 


Metals. 

Therms. 

Cadmium 

—  0.616 

Iron      .... 
Nickel  .... 

—3-6I3 
4.362 

Platinum 
Silver   .... 
Zinc      .... 

0.320 
—0.413 
-0-585 

CdtoCdSC-4 
Cu  to  CuSO4 

4.29 
—  1-4 

Ag  to  AgNO8      . 
Zn  to  ZnSO4 

7-53 
—2.14 

I  S«r  ei'  "  Wied'  Ann'"  vo1-  24,  P-  634. 
"  Wied.  Ann."  vol.  34,  p.  767 
"Ann.  de  Chim.  et  de  Phys."  ()  vol. 


SMITHSONIAN  TABLES. 


10,  p.  201. 

Zn 


Metals. 

Therms. 

Antimony  (Becquerel's)  § 
(commercial) 

13.02 

4.8 

Bismuth  (pure) 
"         (Becquerel's)  || 

I9.I 
25.8 

Cadmium        .... 
German  silver        ..'.'. 

0.46 
2.47 

iron        
Zinc        .... 

2-5 

°-39 

250 


TABLE  262, 


CONDUCTIVITY   OF    THREE-METAL   AND    MISCELLANEOUS   ALLOYS. 


Conductivity  Ct=  C0  (i  +  at-\-  bP). 


Metals  and  alloys. 

Composition  by  weight. 

10* 

*« 

«* 

| 

Gold-copper-silver  .     .    . 

58.3  Au+  26.5  Cu-f  I5.2  Ag 
66.5  Au  -f  15.4  Cu  -f  18.1  Ag 
7.4  Au  +  78.3  Cu+  14.3  Ag 

6.83 

28.06 

574 
529 
1830 

924 
7280 

i 

i 

Nickel-copper-zinc  .    .     . 

(  12.84  Ni  -f  30.59  Cu  -f       ) 
\  6.57  Zn  by  volume    .     .     .  } 

4.92 

444 

51 

i 

Brass      

Various 

T  ^  '?—  T  C  f\ 

I_  -7  \X    T/^3 

"      hard  drawn     .     .     . 

70.2  Cu-f  29.8  Zn   .... 

16.4—  '1  S.U 
12.  ID 

—  /\  iO 

I 

2 

3 

"      annealed    .... 

**        .... 

14-35 

- 

- 

3 

German  silver      .... 

Various 

•5—C 

(  60.  1  6  Cu-f  25.37  Zn-f         ) 
J  14.03  Ni-f  .30  Fe  with  trace  > 
(  of  cobalt  and  manganese  .  ) 

J     J 

3-33 

360 

- 

4 

Aluminium  bronze  .    .     . 

- 

7.5-8.5 

5-7  X  io2 

- 

2 

Phosphor  bronze      .     .     . 

- 

10-20 

- 

- 

2 

Silicium  bronze  .... 

- 

41 

- 

- 

5 

Manganese-copper  . 

30  Mn  -f  70  Cu  .... 

I.OO 

40 

N  ickel-man  ganese-copper 

3  Ni  -f  24  Mn  +  73  Cu    .    . 

2.10 

—30 

- 

4 

(  18.46  Ni  +  61.63  Cu-f         ) 

<  19.67  Zn  -f  0.24  Fe  -f 

•5  f\T 

^nn 

(  0.19  Co  -f  o.iSMn    .     .     .) 

(25.  i  Ni-f  74.41  Cu-f           ) 

Patent  nickel  

<  0.42  Fe  -f  0.23  Zn  -f 

*>  ri*7 

IQO 

(0.13  Mn  -f  trace  of  cobalt   ) 

•jp* 

(53.28  Cu-f  25.31  Ni-f         ) 

<  16.89  Zn  T  446  Fe  -f 

T  on 

.     JQ 

t  o  77  Mn                                    i 

1 

Copper-manganese-iron    . 

91  Cu  -f  7.1  Mn  -f  1.9  Fe 
70.6  Cu  -f  23.2  Mn  -f  6.2  Fe 

4.98 

120 

22 

- 

6 
6 

«(                     «                  « 

69.7  Cu  -f  29.9  Ni  -f  36  Fe  . 

2.60 

120 

- 

7 

Temp.  C.° 

Manganin   

84Cu+  i2Mn  +  4Ni 

2.33 

25 

IO-2O 

8 

<< 

«                           « 

14 

20-30 

8 

ci 

<«             «             n 

• 

4 

30-35 

8 

M 

u             a             « 

i 

•5 

8 

u 

«             <«             « 

, 

J 
I 

io-AC 

8 

(( 

<«                     u                     « 

• 

__2 

45-50 

8 
8 

U 

u 

««.           «             « 

H 

—  4 

w-o8 

8 

T- 

1  Matthieson.              8  W.  Siemens.                            6  Van  der  Ven.            7  Feusner. 

2  Various.                    4  Feusner  and  Lindeck.            6  Blood.                        8  Lindeck. 

SMITHSONIAN  TABLES. 


251 


TABLE  263, 


CONDUCTING    POWER    OF   ALLOYS, 


This  table  shows  the  conducting  power  of  alloys  and  the  variation  of  the  conducting  power  with  temperature.* 
The  values  of  C0  were  obtained  from  the  original  results  by  assuming  silver  :=  ^7^  mhos.  The  conductivity  is 
taken  as  Ct  =  C0  (r  —  o*-f  /3/2),  and  the  range  of  temperature  was  from  o°  to  100°  C. 

The  table  is  arranged  in  three  groups  to  show  (i)  that  certain  metals  when  melted  together  produce  a  solution 
which  has  a  conductivity  equal  to  the  mean  of  the  conductivities  of  the  components,  (2)  the  behavior  of  those 
metals  alloyed  with  others,  and  (3)  the  behavior  of  the  other  metals  alloyed  together. 

inted  out  that,  with  a  few  exceptions,  the  percentage  variation  between  o°  and  100°  can  be  calculated  from  the 

formula  />  —  /*„  —  where/  is  the  observed  and  /'  the  calculated  conducting  power  of  the  mixture  at  100°  C., 
and  Pe  is  the  calculated  mean  variation  of  the  metals  mixed. 


It  is  poi 


Weight  % 

Vo  lume  % 

Variation  per  100°  C. 

of  first  named. 

I04 

Observed. 

Calculated. 

GROUP  i. 

Sn6Pb    

77.O4 

83.96 

7.C7 

8  o 

8670 

30  18 

2Q  67 

Sn4Cd   

8-7  41 

83  10 

Q  l8 

^nXn 

1  1870 

2889 

-3O  O1 

SnZn     

78.06 

77.71 

10.56 

3880 

8720 

3O.I2 

o^'^J 
1O  1  6 

PbSn     

/ 

64.13 

53-41 

6.40 

3780 

8420 

29.41 

29.10 

ZnCd2    

24.  ?6 

26  06 

16  16 

8000 

2986 

•7Q  67 

SnCd4   .... 

23.50 

13-67 

3850 

9410 

29.08 

CdPbg 

7-37 

10-57 

5.78 

35°° 

7270 

27.74 

27.60 

GROUP  2. 

Lead-silver  (Pb2nAg)   . 
Lead-silver  (PbAg) 
Lead-silver  (PbAg2)    . 

95-05 
48.97 

32-44 

94.64 
46.90 
30-64 

5-6o 
8.03 
13.80 

3630 
1960 
1990 

7960 
3100 
2600 

28.24 
16.53 
I7-36 

19.96 

7-73 
10.42 

Tin-gold  (Sni2Au)  .     . 
"      "     (Sn5Au)    .     . 

77-94 
59-54 

90.32 

79-54 

5-20 

3-03 

3080 
2920 

6640 
6300 

24.20 
22.00 

14.83 

5-95 

Tin-copper      .... 

92.24 

80.58 

93-57 
83.60 

7-59 
8.05 

3680 
3330 

8130 
6840 

28.71 
26.24 

19.76 

H-57 

'                  t  .     .     .     . 
t.     .     .     . 
t.     .     .     . 

12.49 
10.30 
9.67 

14.91 

12.35 
n.oi 

5-57 
6.41 
7.64 

8 

691 

294 
1185 
3°4 

5.18 
5-48 
6.60 

3-99 
4.46 
5.22 

t  .     .     .     . 

4.96 

6.O2 

12.44 

995 

705 

9-25 

7-83 

'          "       t  .     .     .     . 

l-I5 

1.41 

39-41 

2670 

5070 

21-74 

20-53 

Tin-silver  ... 

91.30 

96.52 

7.81 

Q  f.c 

3820 

8190 

30.00 

23-31 

«       « 

5J-  5 

75-51 

377° 

°55° 

Zinc-copper  t      .    .     . 

36.70 

42.06 

13-75 

1370 

1340 

12.40 

11.29 

"        "        t      .     .     . 

25.00 

29-45 

13.70 

1270 

1240 

11.49 

10.08 

"        t      .    .     . 

16.53 

23.61 

13-44 

1880 

1800 

12.80 

12.30 

"        t     .     .     . 

8.89 

10.88 

29.61 

2040 

3030 

17.41 

17.42 

"        "        t      .     .     . 

4.06 

5-03 

38-09 

2470 

4100 

20.61 

20.62 

NOTE.  —  Barus,  in  the  "  Am.  Jour,  of  Sci."  vol.  36,  has  pointed  out  that  the  temperature  variation  of  platinum 
alloys  containing  less  than  10%  of  the  other  metal  can  be  nearly  expressed  by  an  equation  y  —  ^—m,  where  y  is  the 
temperature  coefficient  and  x  the  specific  resistance,  m  and  n  being  constants.  If  a  be  the  temperature  coefficient  aX 
o°  C.  and  *  the  corresponding  specific  resistance,  s  (a.  +  m)  =  n. 

For  platinum  alloys  Barus's  experiments  gave  m  =  —  .000194  and  n  =  . 0378. 

For  steel  m  =  —.000303  and  n  —  .0620. 
Matthieson's  experiments  reduced  by  Barus  gave  for 

Gold  alloys  m  —  —  .000045,  n  •=.  .00721. 

Silver     "     m  =  —  .000112,  n  =  . 00538. 

Copper  "     m  =  —  .000386,  n  =  .00055. 

*  £romjhe  experiments  of  Matthieson  and  Vogt,  "  Phil.  Trans.  R.  S."  v.  154. 
T  Hard-drawn. 


SMITHSONIAN  TABLES. 


252 


TABLE  263, 


CONDUCTING    POWER    OF   ALLOYS. 


GROUP  3. 

Alloys. 

Weight  % 

Volume  % 

I04 

aXio« 

*j. 

Variation  per  100°  C. 

of  first  named. 

Observed. 

Calculated. 

Gold-copper  t     .     .    . 

99-23 

98-36 

35-42 

2650 

46§0 

21.87 

23.22 

t     .    .    . 

90-55 

81.66 

10.16 

749 

81 

7.41 

7-53 

Gold-silver  t       ... 

87-95 

79-86 

13.46 

1090 

793 

10.09 

9-65 

"      * 

87.95 

79.86 

13.61 

1140 

1160 

IO.2I 

9-59 

"    t     !  !  ! 

64.80 

52.08 

9.48 

673 

246 

6.49 

6.58 

"    * 

64.80 

52.08 

9-51 

721 

495 

6.7I 

6.42 

"    t    ... 

31-33 
31-33 

19.86 
19.86 

13.69 
13-73 

885 
908 

8.23 
8-44 

8.62 
8.31 

Gold-copper  t     .     .    . 

34.83 

19.17 

12.94 

864 

570 

8.07 

8.18 

"       t     .     .     . 

1.52 

0.71 

53-02 

3320 

7300 

25.90 

25.86 

Platinum-silver  t     .     • 

33-33 

19.65 

4.22 

330 

208 

3.10 

3-21 

"      t     .     . 

9.81 

5-05 

11.38 

774 

656 

7.08 

7-25 

11     t     .     . 

5.00 

2.51 

19.96 

1240 

1150 

11.29 

11.88 

Palladium-silver  t   .     . 

25.00 

23.28 

5-38 

324 

154 

340 

4.21 

Copper-silver  t    .     .     . 

98.08 

98.35 

56.49 

345° 

7990 

26.50 

27.30 

"      t    • 

94.40 

95-  *  7 

51.93 

325° 

6940 

25-57 

25.41 

"      t    .     .    . 

76.74 

77.64 

44.06 

3°3° 

6070 

24.29 

21.92 

«      t    .     .     . 

42-75 

46.67 

47-29 

2870 

5280 

22.75 

24.00 

"      t    .     .     . 
"      t    .     .    . 

7.14 

8.25 
J-53 

50.65 
50-30 

2750 
4120 

4360 
8740 

23.17 
26.51 

25-57 
29.77 

Iron-gold  t      .     .     .     . 

13-59 

27-93 

1-73 

3490 

70IQ 

27.92 

14.70 

"       "     t      .     .     .    . 

9.80 

21.18 

1.26 

2970 

I22O 

I7-55 

1  1.  20 

"       "     t     .     .     .     . 

4.76 

10.96 

1.46 

487 

I03 

3-84 

13.40 

Iron-copper  t      .    .     • 

0.40 

0.46 

24.51 

'55° 

2090 

13-44 

14.03 

Phosphorus-copper  t  . 

2.50 

- 

4.62 

476 

'45 

- 

- 

it                                     U              + 

o-95 

— 

14.91 

1320 

1640 

— 

- 

Arsenic-copper  t     .     . 

5-40 

_ 

3-97 

516 

989 

- 

- 

"       t     .     . 

2.80 

— 

8.12 

736 

446 

— 

— 

«       t     .     • 

trace 

38-52 

2640 

4830 

*  Annealed. 
SMITHSONIAN  TABLES. 


f  Hard-drawn. 


253 


TABLE  264. 


SPECIFIC   RESISTANCE    OF    METALLIC   WIRES, 


This  table  is  modified  from  the  table  compiled  by  Jenkin  from  Matthieson's  results  by  taking  the  resistance  of  silver, 
gold,  and  copper  from  the  observed  metre  gramme  value  and  assuming  the  densities  found  by  Matthieson,  namely, 
10.468,  19.265,  and  8.95. 


Substance. 

Resistance  at  o°  C.  of  a 
wire  one  cm.  long,  one 
sq.  cm.  in  section. 

C8 
°.   M 

v  £  u 

Resistance  at  o°  C.  of  a 
wire  one  metre  long, 
weighing  one  gramme. 

Resistance  at  o°  C.  of  a 
wire  one  foot  long, 
IGSTS  in.  in  diam. 

Resistance  at  o°  C.  of  a 
wire  one  foot  long, 
weighing  one  grain. 

Percentage  increase  of 
resistance  for  iu  C.  in- 
crease of  temp,  at  20°  C.  1 

Silver  annealed  . 

1.460  X  lo"6 

0.01859 

.1523 

8.781 

.2184 

0-377 

"      hard  drawn 

1.585       " 

0.02019 

.1659 

9-538 

.2379 

- 

Copper  annealed 

1.584      " 

002017 

.1421 

9.529 

•2037 

0.388 

"     hard  drawn     . 

1.619      " 

0.02062 

.1449 

9.741 

.2078 

- 

Gold  annealed    . 

2.088       " 

0.02659 

.4025 

12.56 

.5771 

0.365 

"    hard  drawn 

2.125       " 

0.02706 

.4094 

12.78 

.5870 

- 

Aluminium  annealed  . 

2.906      " 

0.03699 

.0747 

17.48 

.IO7I 

- 

Zinc  pressed 

5.613       " 

0.07146 

.4012 

33-76 

•5753 

0-365 

Platinum  annealed      .        * 

9-035       " 

0.1150 

1-934 

54.35 

2-772 

- 

Iron 

9.693       " 

0.1234 

-7551 

58.31 

1.083 

- 

Nickel 

12.43         " 

0.1583 

1-057 

74.78 

1.515 

- 

Tin  pressed         .        .        . 

13.18         " 

0.1678 

.9608 

79.29 

1-377 

0-365 

Lead     "             ... 

19.14         " 

0.2437 

2.227 

II5.I 

3-193 

0.387 

Antimony  pressed 

35-42       " 

0.4510 

2-379 

213.1 

3.410 

0.389 

Bismuth         " 

130.9 

1.667 

12.86 

787.5 

18.43 

0-354 

Mercury         " 

94.07       « 

1.198 

12.79 

565.9 

18.34 

0.072 

Platinum-silver,  2  parts  Ag,  ) 
' 

i  part  Ft,  by  weight        .  ) 

24-33       " 

0.3098 

2.919 

146.4 

4.186 

0.031 

German  silver     . 

20.89      " 

0.2660 

1.825 

125-7 

2.617 

0.044 

Gold-silver,  2  parts  Au,     ) 

i  part  Ag,  by  weight       .  ) 

10.84       " 

0.1380 

1.646 

65.21 

2-359 

0.065 

SMITHSONIAN  TABLES. 


254 


TABLE  265. 


SPECIFIC  RESISTANCE  OF  METALS. 


The  specific  resistance  is  here  given  as  the  resistance,  in  microhms,  per  centimetre  of  a  bar  one  square  centimetre  in 

cross  section. 


Substance. 

Physical  state. 

Specific  resistance. 

Temp.  C. 

Authority. 

Aluminium 

_ 

2.9-4.5 

0 

Various. 

Antimony  . 

Solid 

354-45-8 
182.8 

O 
Melting-point 

De  la  Rive. 

" 

Liquid 

129.2 

• 

'* 

• 

— 

137-7 

860 

« 

Arsenic 

_ 

33-3 

0 

Matthieson  and 

Vogt. 

Bismuth     . 

Electrolytic  soft 

108.0 

o 

Van  Aubel. 

" 

hard 

108.7 

0 

* 

" 

Commercial 

110-268 

0 

Various. 

Boron    .     . 

Pulverized  and  com- 

pressed 

8  X  id0 

_ 

Moissan. 

Cadmium  . 

_ 

6.2-7.0 

_ 

Various. 

" 

Solid 

16.5 

318 

Vassura. 

" 

Liquid 

37-9 

318 

« 

Gold      .    , 

— 

2.04-2.09 

0 

Various. 

Calcium 

- 

7-5 

1  6.8 

Matthieson. 

Cobalt  .     . 

— 

9.8 

0 

" 

Copper  .     . 

Commercial 

1.58-2.20 

0 

Various. 

Iron  .     .    . 

M 

9.7-12.0 

o 

it 

« 

Electrolytic 

« 

II.  2 

I05-5 

Ordinary 
Red  heat 

Kohlrausch. 

(4 

« 

« 

114.8 

Yellow  heat 

(( 

• 

« 

118.3 

Iron  magnetic 

heat 

(( 

Steel.    .    . 

Cast 

19.1 

Ord.  temp. 

<« 

"... 

« 

85.8 

Red  heat 

« 

" 

it 

104.4 

Yellow  heat 

« 

"... 

« 

"3-9 

Nearly  white 

heat 

|| 

<«              \ 

Tempered  glass  hard 

45.7  (i  -f  .00161;) 

t 

Barus  and 
Strouhal. 

« 
« 

"          light  yellow 
"                  yellow 

28.9  (i  +  .00244;) 
26.3(1  +  .00280;) 

't 
t 

«              « 
(i 

« 

"                  blue 

20.5  (  i  -j-  .00330;) 

t 

(i 

"... 

"          light  blue 

18.4(1  +  .00360;) 

t 

« 

« 

soft 

15.9  (i  +  .00423;) 

t 

« 

Iron  .     .     . 

Cast,  hard 

97.8 

0 

hi 

« 

"      soft 

74-4 

0 

M 

Indium  . 

838 

0 

Erhard. 

Lead      .     . 
Lithium 

- 

18.4-19.6 
8.8 

o 

20 

Various. 
Matthieson. 

Magnesium 

- 

4.1-5.0 

0 

Various. 

Nickel  .     . 

— 

10.7-12.4 

0 

" 

Palladium  . 

_ 

10.6-13.6 

0 

M 

Platinum    . 
Potassium  . 

— 

9.0-15.5 
25.1 

o 
o 

H 

Matthieson. 

H 

Fluid 

504 

100 

Silver     .     . 

I-5-1-? 

0 

Various. 

Strontium  . 

_ 

25-J3 

20 

Matthieson. 

Tellurium  . 
« 

- 

2.17  X  io5 
55-05 

19-6 
294 

« 

Vincentini  and 
Omodei. 

Tin    .     .    . 

_ 

9-  53-"  -4 

0 

Various. 

H 

_ 

9-53 

0 

Vassura. 

« 

Solid 

£ 
20.96 

226.5 

* 

"          .        .        . 

Liquid 

44-56 

226.5 

" 

Zinc  .     .     . 

Solid 

c.  C6-6.O4 
18.16 

o 
Melting-point 

De  la  Rive. 

« 

Liquid 

36.00 

SMITHSONIAN  TABLES. 


255 


TABLE  266, 


RESISTANCE    OF    METALS   AND 

The  electrical  resistance  of  some  pure  metals  and  of  some  alloys  have  been  determined  by  Dewar  and  Fleming  and 
increases  as  the  temperature  is  lowered.  The  resistance  seems  to  approach  zero  for  the  pure  metals,  but  not  for 
temperature  tried.  The  following  table  gives  the  results  of  Dewar  and  Fleming.* 

When  the  temperature  is  raised  above  o°  C.  the  coefficient  decreases  for  the  pure  metals,  as  is  shown  by  the  experi- 
experiments  to  be  approximately  true,  namely,  that  the  resistance  of  any  pure  metal  is  proportional  to  its  absolute 
is  greater  the  lower  the  temperature,  because  the  total  resistance  is  smaller.  This  rule,  however,  does  not  even 
zero  Centigrade,  as  is  shown  in  the  tables  of  resistance  of  alloys.  (Cf.  Table  262.) 


Temperature  = 

100° 

20° 

0° 

—  80° 

Metal  or  alloy. 

Specific  resistance  in  c.  g.  s.  units. 

Aluminium,  pure  hard-drawn  wire  .        .    •    . 

4745 

3505 

3161 

- 

Copper,  pure  electrolytic  and  annealed  . 

1920 

1457 

1349 

- 

Gold,  soft  wire         

2665 

2081 

1948 

1400 

Iron,  pure  soft  wire      .^.»,'^>        •  ;       •     *?»,l 

13970! 

9521 

8613 

- 

Nickel,  pure  (prepared  by  Mond's  process  ) 
from   compound  of  nickel  and  carbon  >  . 
monoxide)                                                    ) 

19300 

13494 

12266 

7470 

IOQO7 

87  C2 

§221 

6 

Silver,  pure  wire      .        .        .        .        •     ,«  . 

ivjyu/ 

2139 

°7o* 

1647 

1559 

1138 

13867 

10473 

9575 

6681 

German  silver,  commercial  wire      .        .      "... 

35720 

34707 

34524 

33664 

Palladium-silver,  20  Pd  +  80  Ag     .      ;/,    ,    .  . 

15410 

14984 

14961 

14482 

Phosphor-bronze,  commercial  wire          ,        . 

9071 

8588 

8479 

8054 

Platinoid,  Martino's  platinoid  with  i  to  2%  ) 
tungsten                                                       [  ' 

44590 

43823 

43601 

43022 

Platinum-iridium,  80  Pt  -f-  20  Ir 

31848 

29902 

29374 

275°4 

Platinum-rhodium,  90  Pt  -f-  10  Rh  . 

18417 

14586 

13755 

10778 

Platinum-silver,  66.7  Ag  +  33.3  Pt  . 

27404 

26915 

26818 

26311 

Carbon,  from  Edison-Swan  incandescent  ) 
lamp                                                              j  • 

- 

4046X  io8 

4092X108 

4189X108 

Carbon,  from  Edison-Swan  incandescent  \ 
lamp                                                              f  • 

3834X108 

3908X108 

3955Xio8 

4054X108 

Carbon,  adamantine,  from  Woodhouse  and  ) 
Rawson  incandescent  lamp                        )  ' 

6168X108 

6300X108 

6363X108 

6495X108 

"  Phil.  Mag."  vol.  34,  1892. 
t  This  is  given  by  Dewar  and  Fleming  as  13777  for  96°.4,  which  appears  from  the  other  measurements  too  high. 


SMITHSONIAN  TABLES. 


256 


TABLE  266, 


ALLOYS   AT   LOW   TEMPERATURES. 


by  Cailletet  and  Bouty  at  very  low  temperatures.  The  results  show  that  the  coefficient  of  change  with  temperature 
the  alloys.  The  resistance  of  carbon  was  found  by  Dewar  and  Fleming  to  increase  continuously  to  the  lowest 

ments  or  Miiller,  Benoit,  and  others.  Probably  the  simplest  rule  is  that  suggested  by  Clausius,  and  shown  by  these 
temperature.  This  gives  the  actual  change  of  resistance  per  degree,  a  constant ;  and  hence  the  percentage  of  change 
approximately  hold  for  alloys,  some  of  which  have  a  negative  temperature  coefficient  at  temperatures  not  far  from 


1  

Temperature  — 

—  100° 

—  182° 

-197° 

Mean  value  of 
temperature  co- 
efficient between 
—  100°  and 

-f  100°  C.* 

Metal  or  alloy. 

Specific  resistance  in  c.  g.  s.  units. 

Aluminium,  pure  hard-drawn  wire 

1928 

894 

- 

.00446 

1    Copper,  pure  electrolytic  and  annealed  . 

757 

272 

I78 

431 

Gold,  soft  wire         .        .        .        .        . 

1207 
4010 

6110 

5295 
962 

567i 
3328o 

604 
1067 

1900 

2821 

472 
2553 

32512 

608 
220XD 

375 
578 

538 

34i 

377 
428 

035 

Nickel,  pure  (prepared  by  Mond's  process  ) 
from   compound  of   nickel  and  carbon  >  . 
monoxide)                                                      ) 

Silver,  pure  wire       

German  silver,  commercial  wire 

Palladium-silver,  20  Pd  -f  80  Ag     . 

14256 

13797 

- 

039 

Phosphor-bronze,  commercial  wire  . 

7883 

737i 

- 

070 

1    Platinoid,  Martino's  platinoid  with  I  to  2%  ) 
tungsten                                                          ) 

42385 

4U54 

- 

025 

Platinum-iridium,  80  Pt  -f  20  Ir 

26712 

24440 

- 

087 

Platinum-rhodium,  90  Pt  +  10  Rh  . 

9834 

7U4 

- 

312 

Platinum-silver,  66.7  Ag  +  33.3  Pt  . 

26108 

25537 

- 

024 

Carbon,  from  Edison-Swan  incandescent  ) 
lamp                                                              ) 

42i8Xio8 

432iXio3 

- 

- 

Carbon,  from  Edison-Swan  incandescent  ) 
lamp                                                             f 

4079  X  i  o3 

4i8oXio8 

- 

031 

Carbon,  adamantine,  from  Woodhouse  and  \ 
Rawson  incandescent  lamp                        f 

6533X10^ 

- 

- 

029 

n  _         n 

*  This  is  a  in  the  equation  R  —  R0  (i  -f  at),  as  calculated  from  the  equation  a  == — "^  R~l< 


SMITHSONIAN  TABLES. 


257 


TABLE  267. 


EFFECT    OF    ELONGATION    ON    THE    SPECIFIC    RESISTANCE    OF    SOFT 

METALLIC   WIRES.* 


Substance. 

Increase  of  specific  resistance  for  i  %  of  elongation  — 

Permanent  elongation. 

Elastic  elongation. 

From  .50  %  to  .60  % 
"      .70  "  "  .80  •' 
«      .50"  ".55" 

From  2.5  %  to  7.7  % 
"      4.6  "   "  4.8  " 
"      0.7  "   "  1.0  " 

Iron      
German  silver       .... 

TABLE  268. 

EFFECT  OF  ALTERNATING   THE  CURRENT  ON    ELECTRIC  RESISTANCE, 

This  table  gives  the  percentage  increase  of  the  ordinary  resistance  of  conductors  of  different  diameters 
when  the  current  passing  through  them  alternates  with  the  periods  stated  in  the  last  column. t 


Diameter  in  — 

Area  in  — 

Percentage  increase  of 
ordinary  resistance. 

Number  of 
complete 
periods  per 
second. 

Millimetres. 

Inches. 

Sq.  mm. 

Sq.  in. 

JO 

•3937 

78.54 

.122 

• 
Less  than  ^ 

15 

.5905 

176.7 

.274 

2-5 

20 

.7874 

314.16 

.487 

8 

25 

.9842 

490.8 

.760 

17-5 

80 

40 

J-575 

1256 

i-95 

68 

100 

3-937 

7854 

12.17 

3.8  times 

1000 

39-39 

785400 

1217 

35  times 

J 

9 

•3543 

63.62 

.098 

Less  than  ^ 

^ 

134 
18 

.5280 
.7086 

I4I-3 
254-4 

.218 
•394 

2-5 
8 

100 

22.4 

.8826 

394 

.611 

17-5 

775 

•3OI3 

47.2 

.071 

Less  than  ^ 

11.61 

15-5 

•4570 
.6102 

106 
189 

.164 
.292 

2-5 

8 

133 

19.36 

.7622 

294 

•456 

17-5 

SMITHSONIAN  TABLES. 


*  T.  Gray,  "Trans.  Roy.  Soc.  Edin."  1880. 
t  W.  M.  Mordey,  "  Inst.  El.  Eng.  London,"  i! 


258 


TABLES  269,  27O. 
CONDUCTIVITY   OF    ELECTROLYTIC   SOLUTIONS. 

This  subject  has  occupied  the  attention  of  a  considerable  number  of  eminent  workers  in 
molecular  physics,  and  a  few  results  are  here  tabulated.  It  has  seemed  better  to  confine  the 
examples  to  the  work  of  one  experimenter,  and  the  tables  are  quoted  from  a  paper  by  F.  Kohl- 
rausch,*  who  has  been  one  of  the  most  reliable  and  successful  workers  in  this  field. 

The  study  of  electrolytic  conductivity,  especially  in  the  case  of  very  dilute  solutions,  has  fur- 
nished material  for  generalizations,  which  may  to  some  extent  help  in  the  formation  of  a  sound 
theory  of  the  mechanism  of  such  conduction.  If  the  solutions  are  made  such  that  per  unit 
volume  of  the  solvent  medium  there  are  contained  amounts  of  the  salt  proportional  to  its  electro- 
chemical equivalent,  some  simple  relations  become  apparent.  The  solutions  used  by  Kohlrausch 
were  therefore  made  by  taking  numbers  of  grammes  of  the  pure  salts  proportional  to  their  elec- 
trochemical equivalent,  and  using  a  litre  of  water  as  the  standard  quantity  of  the  solvent.  Tak- 
ing the  electrochemical  equivalent  number  as  the  chemical  equivalent  or  atomic  weight  divided 
by  the  valence,  and  using  this  number  of  grammes  to  the  litre  of  water,  we  get  what  is  called 
the  normal  or  gramme  molecule  per  litre  solution.  In  the  table,  m  is  used  to  represent  the 
number  of  gramme  molecules  to  the  litre  of  water  in  the  solution  for  which  the  conductivities 
are  tabulated.  The  conductivities  were  obtained  by  measuring  the  resistance  of  a  cell  filled  with 
the  solution  by  means  of  a  Wheatstone  bridge  alternating  current  and  telephone  arrangement. 
The  results  are  for  18°  CM  and  relative  to  mercury  at  o°  C.,  the  cell  having  been  standardized  by 
filling  with  mercury  and  measuring  the  resistance.  They  are  supposed  to  be  accurate  to  within 
one  per  cent  of  the  true  value. 

The  tabular  numbers  were  obtained  from  the  measurements  in  the  following  manner  :  — 

Let  A"x  8  =  conductivity  of  the  solution  at  18°  C.  relative  to  mercury  at  o°  C. 

ATg  =  conductivity  of  the  solvent  water  at  18°  C.  relative  to  mercury  at  o°  C. 

Then  A^8  — A~"a  =  &la  =  conductivity  of  the  electrolyte  in  the  solution  measured. 

_!«.  =  y,  =  conductivity  of  the  electrolyte  in  the  solution  per  molecule,  or  the  "  specific 
molecular  conductivity." 


TABLE  269.  —Value  of  fclg  for  a  few  Electrolytes. 

This  short  table  illustrates  the  apparent  law  that  the  conductivity  in  very  dilute  solutions  is  proportional  to  the 

amount  of  salt  dissolved. 


m 

KC1 

NaCl 

AgN03 

KC2H3O2 

K2S04 

MgS04 

O.OOOOOI 

1.216 

1.024 

I.oSo 

0-939 

i-27S 

1.056 

O.OOOO2 

0.00006 

2.434 
7.272 

2.056 
6.162 

2.146 
6.462 

1.886 
5.610 

2.532 
7-524 

2.104 
6.216 

0.000  1 

12.09 

10.29 

10.78 

9-34 

12.49 

10.34 

TABLE  270.  —Electro-Chemical  Equivalents  and  Normal  Solutions. 

The  following  table  of  the  electro-chemical  equivalent  numbers  and  the  densities  of  approximately  normal  solutions 
of  the  salts  quoted  in  Table  271  may  be  convenient.  They  represent  grammes  per  cubic  centimetre  of  the  solution 
at  the  temperature  given. 


Salt  dissolved. 

Grammes 
per  litre. 

m 

Temp. 

Density. 

Salt  dissolved. 

Grammes 
per  litre. 

M 

Temp. 
C. 

Density. 

KC1     .     .     . 

74-59 

I.O 

15.2 

1-0457 

£K2SO4     . 

87.16 

I.O 

18.9 

1.0658 

NH4C1    .     . 

53-55 

1.0009 

18.6 

1.0152 

iNa2SO4  . 

71.09 

I.OOO3 

1  8.6 

1.  0602 

NaCl  .     .     . 

58-50 

I.O 

18.4 

1.0391 

|Li2SO4     . 

55-09 

I.OOO7 

18.6 

1.0445 

LiCl    .     .     . 

42.48 

ib 

18.4 

I.O227 

|MgS04    . 

60.17 

1.0023 

18.6 

I-°573 

JBaCl2    .     . 

104.0 

I.O 

18.6 

1.0888 

£ZnSO4     . 

80.58 

I.O 

5-3 

1.0794 

iZnCl2     .     . 

68.0 

I.OI2 

15.0 

1.0592 

iCuSO4     . 

79-9 

I.OOI 

18.2 

1.0776 

KI.     .     .     . 

165.9 

I.O 

18.6 

1.1183 

|K2CO8    . 

69.17 

1.  0006 

18.3 

1.0576 

KN03     .     . 

101.17 

I.O 

18.6 

1.  060  1 

fNaaCOs  . 

53-04 

I.O 

17.9 

1.0517 

NaNO3   .     . 

85.08 

I.O 

18.7 

1.0542 

KOH    .    . 

56.27 

1.0025 

1  8.8 

1.0477 

AgN03    .    . 
iBa(N03)2  . 
KC1O3     -     . 

169.9 
65.28 
61.29 

I.O 

o-5 
o-5 

18.3 

1.0367 

HC1      .     . 
HNO3  .     . 
iH2S04     . 

36.51 
63.13 
49.06 

1.0041 
1.0014 
1.  0006 

18.6 
18.6 
18.9 

1.0161 
1.0318 
1.0300 

KC2H302     . 

98.18 

1.0005 

18.6 

1.0467 

SMITHSONIAN  TABLES. 


;  Wied.  Ann."  vol.  26,  pp.  161-226. 
259 


TABLE  271. 

SPECIFIC    MOLECULAR   CONDUCTIVITY  ft:   MERCURY=  1O8, 


Salt  dissolved. 

W=  10 

5 

3 

I 

o-5 

O.I 

.05 

•03 

.01 

iK2SO4    . 

_ 

_ 

_ 

_ 

672 

736 

897 

959 

1098 

KC1 

_ 

_ 

827 

919 

958 

1047 

1083 

1107 

"47 

KT  .          ... 

_ 

770 

968 

997 

1069 

IIO2 

1123 

1161 

NH4C1     . 

- 

752 

825 

907 

948 

1035 

1078 

IIOI 

1142 

KNO3      . 

- 

572 

752 

839 

983 

1037 

1067 

1122 

!    KC103     '.        '.        ! 

- 

- 

487 

658 

725 
799 

861 
927 

904 
(976) 

939 
1006 

IOO6 
1053 

£Ba2N206        .        . 

- 

- 

- 

- 

53J 

755 

828 

(870) 

951 

|CuSO4  . 
AgN03    . 

- 

351 

448 

241 
635 

288 
728 

424 
886 

479 
936 

,$, 

675 
1017 

|ZnSO4   . 

_ 

82 

I46 

249 

302 

431 

500 

556 

68S 

|MgSO4  . 

- 

82 

270 

33° 

474 

532 

587 

715 

|Na2SO4 

— 

— 

— 

475 

559 

734 

784 

o2o 

906 

AZnCla     . 

60 

1  80 

280 

5M 

601 

768 

817 

851 

NaCl        . 

398 

528 

69,5 

757 

865 

897 

(920) 

962 

NaNO8    .        . 

_ 

_ 

430 

617 

694 

817 

855 

877 

907 

KC2H302 

3° 

240 

381 

594 

671 

784 

820 

841 

879 

InSo?.    :    : 

660 

1270 

1560 

427 
1820 

510 
1899 

682 
2084 

751 
2343 

799 
2515 

899 

2855 

c2H4o  ;    '.    . 

°-5 

2.6 

5-2 

12 

19 

43 

62 

79 

I32 

HC1         ... 

600 

1420 

2010 

2780 

3017 

3244 

3330 

3369 

34l6 

HNO8     . 

610 

1470 

2O7O 

2770 

2991 

3225 

3289 

3328 

3395 

1H3P04  .        .        . 
KOH       . 

148 
423 

160 
990 

170 

2OO 
1718 

250 
1841 

540 
2045 

620 
2078 

790 
2124 

NH3 

2.4 

3-3 

8.4 

12 

31 

43 

50 

92 

Salt  dissolved. 

.006 

.002 

.001 

.0006 

.0002 

.0001 

.00006 

.00002 

.0000  i 

iK2SO4  .        .        . 
KC1         ... 

1130 
1162 

1181 
1185 

1207 
"93 

1220 

"99 

1241 
I2O9 

1249 
1209 

1254 

1212 

1266 
1217 

1275 
1216 

KI   . 

1176 

"97 

1203 

1209 

1214 

1216 

1216 

1216 

1207 

NH4C1     . 

"57 

1180 

1190 

"97 

1204 

1209 

I2I5 

1209 

1205 

KNO3     . 

1140 

"73 

1180 

1190 

"99 

1207 

1220 

1198 

1215 

|BaCl2     . 
KC1O8     . 

1031 
1068 

1074 
1091 

1092 

IIOI 

1  102 
IIO9 

1118 
1119 

1126 

1122 

"33 
1126 

"44 
"35 

1142 
1141 

£Ba2N2O6 

982 

1033 

1054 

1066 

1084 

1096 

IIOO 

1114 

1114 

^CuSO4  . 

740 

873 

95° 

987 

1039 

1062 

1074 

1084 

1086 

AgN03    . 

1033 

1057 

1068 

1069 

1077 

1078 

1077 

1073 

1080 

^ZnSO4   . 

744 

861 

919 

953 

1001 

1023 

1032 

1047 

1060 

^MgSO4  . 

773 

88  1 

935 

967 

1015 

1034 

1036 

1052 

1056 

^Na2SO4 

933 

980 

998 

1009 

1026 

1034 

1038 

1056 

1054 

^ZnCl2 

939 

979 

'    994 

1004 

1  020 

IO29 

1031 

i°35 

1036 

NaCl 

976 

998 

1008 

1014 

1018 

IO29 

1027 

1028 

1024 

NaNO3    . 

921 

942 

952 

956 

966 

975 

970 

972 

975 

KC2H3O2 

891 

913 

919 

923 

933 

934 

935 

943 

939 

^Na2CO3 

956 

IOIO 

1037 

1046 

988 

874 

790 

7i5 

697* 

|lI2S04  . 

3001 

3240 

3316 

3342 

3280  • 

3118 

2927 

2077 

1413* 

C2H40     . 

170 

283 

380 

470 

796 

995 

"33 

1328 

1304* 

HC1 
HN08     . 

3438 

3455 
3448 

3455 
3427 

3440 
3408 

3340 

3285 

3170 

3088 

2968 
2863 

2057 
1904 

1254* 
"44* 

^H3PO4  . 

858 

945 

968 

977 

920 

837 

746 

497 

402* 

KOH 

2141 

2140 

2IIO 

2074 

1892 

1689 

1474 

845 

747* 

NH3 

116 

190 

260 

330 

500 

610 

690 

700 

560* 

SMITHSONIAN  TABLES. 


*  Acids  and  alkaline  salts  show  peculiar  irregularities. 
26O 


TABLE  272, 
LIMITING  VALUES  OF  ,u- 

This  table  shows  limiting  values  of  /A  =  —  .io8  for  infinite  dilution  for  neutral  salts,  calculated  from  Table  271, 


Salt. 

/* 

Salt. 

M 

Salt. 

M 

Salt. 

/* 

iK2SO4     . 

1280 

iBaCl2      . 

1150 

iMgS04    . 

1080 

iH2S04     . 

3700 

KC1  .    .    . 

I22O 

iKC103     . 

1150 

|Na2SO4  . 

1060 

HC1      .    . 

3500 

KI    .    .    . 

1220 

iBaN206  . 

1120 

iZnCl    .     . 

1040 

HN08.    . 

35°o 

NH4C1  .     . 

I2IO 

iCuSO4     . 

IIOO 

NaCl     .    . 

1030 

£H3P04    . 

IIOO 

KN08  .    . 

1210 

AgN03     . 

1090 

NaNO3      . 

980 

KOH    .    . 

2200 

- 

- 

£ZnSO4     . 

I080 

K2C2H3O2 

940 

iNa2C03  . 

I4OO 

If  the  quantities  in  Table  271  be  represented  by  curves,  it  appears  that  the  values  of  the 
specific  molecular  conductivities  tend  toward  a  limiting  value  as  the  solution  is  made 
more  and  more  dilute.  Although  these  values  are  of  the  same  order  of  magnitude,  they 
are  not  equal,  but  depend  on  the  nature  of  both  the  ions  forming  the  electrolyte. 

When  the  numbers  in  Table  272  are  multiplied  by  Hittorf's  constant,  or  o.oooii,  quan- 
tities ranging  between  0.14  and  o.io  are  obtained  which  represent  the  velocities  in  milli- 
metres per  second  of  the  ions  when  the  electromotive  force  gradient  is  one  volt  per 
millimetre. 

Specific  molecular  conductivities  in  general  become  less  as  the  concentration  is  in- 
creased, which  may  be  due  to  mutual  interference.  The  decrease  is  not  the  same  for 
different  salts,  but  becomes  much  more  rapid  in  salts  of  high  valence. 

Salts  having  acid  or  alkaline  reactions  show  marked  differences.  They  have  small 
specific  molecular  conductivity  in  very  dilute  solutions,  but  as  the  concentration  is  in- 
creased the  conductivity  rises,  reaches  a  maximum  and  again  falls  off.  Kohlrausch  does 
not  believe  that  this  can  be  explained  by  impurities.  H3PO4  in  dilute  solution  seems  to 
approach  a  monobasic  acid,  while  H2SO4  shows  two  maxima,  and  like  H3PO4  approaches 
in  very  weak  solution  to  a  monobasic  acid. 

Kohlrausch  concludes  that  the  law  of  independent  migration  of  the  ions  in  media  like 
water  is  sustained. 


TABLE  273, 


TEMPERATURE  COEFFICIENT. 


The  temperature  coefficient  in  general  diminishes  with  dilution,  and  for  very  dilute  solutions  appears  to  approach  a 
common  value.  The  following  table  gives  the  temperature  coefficient  for  solutions  containing  o.oi  gramme  mole- 
cule of  the  salt. 


Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

KC1  .     .     . 

0.0221 

KI     .     .     . 

O.O2I9 

iK2SO4      . 

0.0223 

|K2C08     .     . 

0.0249 

NH4C1  .     . 
NaCl     .     . 
LiCl.    .    . 
|BaCl2  .     . 
|ZnCl2  .     . 
iMgd2      . 

O.O226 
0.0238 
O.O232 
0.0234 
0.0239 
O.O24I 

KNO3   .     . 

NaNO3  .     . 
AgN03.     . 
iBa(N03)2 
KC103  .     . 
KC2H3O2  . 

0.02  1  6 

0.0226 

O.O22I 
O.O224 
O.O2I9 
0.0229 

iNa2SO4    . 
iLi2S04     . 
iMgS04     . 
iZnSO3      . 
iCuSO4     . 

0.0240 
0.0242 
0.0236 
0.0234 
0.0229 

iNa2CO3  .     . 

0.0265 

KOH    .    .    . 
HC1       .     .     . 
HNO3  .    .     . 
iH2S04     .     . 

0.0194 
0.0159 
0.0162 
0.0125 

iH2S04          ) 
for  m  =  .001  f 

0.0159 

SMITHSONIAN  TABLES. 


26l 


TABLE  274. 

VARIOUS    DETERMINATIONS   OF   THE    VALUE    OF   THE    OHM,  ETC.* 


Observer. 

Date. 

Method. 

Value  of 
B.  A.  U. 
in  ohms. 

Value  of  100 
cms.  of  Hg 
in  B.  A.U. 

Value  of 
ohm  in 
cms.  of  Hg. 

I 

2 

3 
4 

5 
6 

9 

10 

ii 

12 
12 

!3 
14 
IS 

16 
17 

18 
19 

Lord  Rayleigh     . 
Lord  Rayleigh     . 
Mascart  .... 
Rowland      .     .     • 

Kohlrausch     .     . 

Glazebrook     *    •  ; 
Wuilleumeier  .     . 
Duncan  &  Wilkes 
Jones  

Strecker.    .    .    . 
Hutchinson     .     . 
Salvioni  .... 
Salvioni  .... 

H.  F.  Weber  .    . 
H.  F.  Weber  .     . 
Roti        .... 

1882 
1883 
1884 
1887 

1887 

1882  to  1888 
1890 
1890 
1891 

1885 
1888 
1890 

1884 
1884 

1885 
1889 

1883 
1885 

Rotating  coil     .    . 
Lorenz  method  .     . 
Induced  current     . 
Mean     of    several 
methods     .     .     . 
Damping   of  mag- 

.9865! 
.98677 
.98611 

.98644 

.08660 
.98665 
.98686 
.98634 

(-95412) 
•95374 
•95349 

•95338 
•95352 
•95355 
•95341 

•95334 
•95352 
•95332 
•95354 

106.31 

106.27 
106.33 

106.32 

106.32 
106.29 
106.31 
106.34 
106.31 

Induced  currents  . 

Lorenz  method  .    . 
Lorenz  method  .    . 
Mean  .... 

An  absolute  de-1 
termination  of  re- 
sistance was  not 
made.  The  value 
.98656  has  been 
used.                      J 

•986.S3 

106.31 

- 

106.32 
106.30 
106.33 
106.30 

•9  S3  54 

106.31 

Induced  current    . 
Rotating  coil     .     . 
Mean  effect  of  in- 
duced current     . 

Damping  of  mag- 
net     
Damping  of  mag- 
net     
Lorenz  method.     . 

Absolute  measure- 
ments    compared 
with  German  silver 
wire    coils    issued 
by    Siemens     or 
Strecker. 

105-37 

106.16 

105.89 
105.98 

106.24 

106.03 
105.93 

Heinstedt    .    .    . 

Wild  

Lorenz    .... 

The  Board  of  Trade  committee  recommended  for  adoption  the  values  .9866  and  106.3. 
The  specific  resistance  of  mercury  in  ohms  is  thus  .9407  X  lo"4. 
Also  i  Siemens  unit  =    .9407  ohm. 
=    .9S35B.A.U. 
i  ohm    .    .    .  =  1.01358  B.  A.  U. 

1 
ofs 

T. 
Tht 
i  B 

.001 

he  following  values  have  been  foun 
ilver  nitrate  in  one  second  by  a  cur 

Mascart,  "  J.  de  Physique,"  iii. 
Rayleigh,  "  Phil.  Trans."  ii.  i8£ 
Kohlrausch,  "  Wied.  Ann."  xx\ 
T.  Gray,  "  Phil.  Mag."  xxii.  188 
Portier  et  Pellat,  "  J.  de  Physiq 

he  following  values  have  been  foun 
;y  have  been  reduced  from  those  £ 
.  A.  U.  =  .9866  ohm,  and  that  the 
1  18  gramme. 

Rayleigh,  "Trans."  ii.  1884 
Carhart 

d  for  the  mass  of  silver  deposited  from  a 
rent  of  one  ampere  :  — 

1884       .,,       «.       ,        ...       A        .    .ooni5( 

solution 

) 
J 

> 

it  i5°C. 
tion  that 
npere  is 

ii.  1886  ..-.,..     .001118; 
6     about  t  .001118 
ue,"  ix.  1890   001119: 

d  for  the  electromotive  force  of  a  Clark  cell  ; 
riven  in  the  original  papers  on  the  supposi 
mass  of  silver  deposited  per  second  per  ai 

i  4.*?4<;  volt 

T    A?AC\        " 

Kohle,  "  Zeitschrift  fur  Instrumentenkunde,"  1892    .         .         .     1.4341     " 
Glazebrook  and  Skinner,  "  Proc.  R.  S."  Ii.  1892         .         .         .     1.4342     " 

*  Abstract  from  the  Report  of  the  British  Association  Committee  on  Practical  Standards  for  Electrical  Measure- 
ment, "  Proc.  Brit.  Assoc."  1892. 
t  -j;  .0000002  T.  G. 

SMITHSONIAN  TABLES. 

262 


TABLE  275. 


SPECIFIC   INDUCTIVE    CAPACITY   OF   CASES. 


With  the  exception  of  the  results  given  by  Ayrton  and  Perry,  for  which  no  temperature  record  has  been  found,  the 
values  are  for  o°  C.  and  760  mm.  pressure. 


Gas. 

Sp.  ind.  cap. 

Authority. 

Vacuum  =  i. 

Air=i. 

Air         

1.0015 

I.OOOO 

Ayrton  and  Perry 

14 

I.OOCKQ 

I.OOOO 

KlementiC 

a 

I.OOO^Q 

I  OOOO 

Boltzmann 

Carbon  disulphide         .        .        .        . 

I.OO29 

1.0023 

KlemenCiC. 

Carbon  dioxide,  COa     .        .        ,        .   . 

1.0023 

1.0008 

Ayrton  and  Perry. 

«             «        « 

1.00098 

1.00039 

KlemenCiC. 

«             «        « 

I.0009S 

1.00036 

Boltzmann. 

Carbon  monoxide,  CO  . 

1.00069 

I.OOOIO 

KlemenCiC. 

<«              « 

1.00069 

I.OOOIO 

Boltzmann. 

Coal  gas  (illuminating)          ,        . 

I.OOI9 

1.0004 

Ayrton  and  Perry. 

I.OOI3 

0.0008 

Ayrton  and  Perry 

« 

I.OOO26 

0.00067 

KlemenCiC. 

« 

I.OOO26 

0.00067 

Boltzmann. 

Nitrous  oxide,  N2O       .        »        .        . 

I.OOII6 

1.00057 

KlemenCiC. 

«           «        « 

I.OOOQQ 

1.00040 

Boltzmann. 

Sulphur  dioxide     

1.0052 

1.0037 

Ayrton  and  Perry. 

«            « 

1.00955 

1.00896 

KlemenCiC. 

Vacuum  5    mm.  pressure 

1.  0000 

0.9985 

Ayrton  and  Perry. 

"    o.ooi   "          "        about  . 

I.OOOO 

0.94 

Ayrton  and  Perry. 

« 

I.OOOO 

0.99041 

KlemenCiC. 

« 

I.OOOO 

0.99941 

Boltzmann. 

SMITHSONIAN  TABLES. 


263 


TABLE  276. 

SPECIFIC    INDUCTIVE    CAPACITY    OF    SOLIDS   (AIR  =  UNITY). 


Substance. 

Sp.  ind.  cap. 

Authority. 

Calcspar  parallel  to  axis 
"        perpendicular  to  axis 

7-5 
7-7 
2.12-2.34 

Romich  and  Nowak. 
«          «          « 

Schiller. 

"            vulcanized  .        .        .       .  *  ' 
Celluvert,  hard  gray         .        .        . 
"            "     red 

2.69-2.94 
1.19 

1.44 

u 

Elsas. 
tt 

"            "     black       .... 
"         soft  red   

1.89 
2.66 
2.08 

u 

Rossetti. 

« 

•j.iq-^.48 

Boltzmann. 

a 

2.21-2.76 

Schiller. 

« 

2.72 

Winkelmann. 

« 

2.56 

Wullner. 

u 

2.& 

Elsas. 

« 

1.9 

Thomson  (from  Hertz's  vibrations). 

6-7 

Romich  and  Nowak. 

Glass,*  density  2.5  to  4.5 
Double  extra  dense  flint,  density  4.5    . 
Dense  flint,  density  3.66 
Light  flint,         "       3.20 
Very  light  flint  "        2.87 
Hard  crown      "       2.485     . 
Plate                  "           -        ... 

Mirror  
tt 

6.8 
5-10 
9.90 

7-38 
6.70 
6.61 
6.96 

8-45 
5.8-6.34 

Curie. 
Various. 
Hopkinson. 

« 
u 

« 

« 

Schiller. 
Winkelmann. 

(i 

6.88 

Donle. 

Plate     '. 
u 
« 

6.44-7.46 
3.31-4.12 

6.10 

Elsas. 
Schiller. 
Romich  and  Nowak. 
Wullner. 

Guttapercha     
Gypsum   

3-3-4-9 

h3 

6.64 

Submarine  cable  data. 
Curie. 
Klemenc'ic'. 

« 

« 

8.00 
7.98 

Curie. 
Bouty. 

„ 

Elsas. 

u 

Paraffin     
« 

5    4.6 

?$ 

Romich  and  Nowak. 
Boltzmann. 
Gibson  and  Barclay. 

u 

'        quickly  cooled  translucent 
'        slowly  cooled  white   ... 

« 
'        fluid  —  pasty 
solid  
Porcelain          
Quartz,  along  the  optic  axis    .        . 
"       transverse   ...."." 
Resin        .        .         . 
Rock  salt          

Selenium  ....... 

2.29 
1.68-1.92 
1.85-2.47 
2.18 
1.96-2.29 
1.98-2.08 

i-95 
4-38 

4-55 
4.49 
2.48-2.57 
18.0 

5.85 

IO  2 

Hopkinson. 
Schiller.t 

Winkelmann. 
Donle,  Wullner. 

Arons  and  Rubens. 
«         «         «« 

Curie. 

« 

Boltzmann. 
Hopkinson. 
Curie. 

Romich  and  Nowak. 

Shellac      .         .        .        .        .  '-      . 

3.10 
3.67 

2-95-3-73 

Winkelmann. 
Donle. 
Wullner. 

*  The  values  here  quoted  apply  when  the  duration  of  charge  lies  between  0.25  and  0.00005  of  a  second.  J.  J. 
Thomson  has  obtained  the  value  2.7  when  the  duration  of  the  charge  is  about  i  /  25  X  io6  of  a  second  ;  and  this  is 
confirmed  by  Blondlot,  who  obtained  for  a  similar  duration  2.8. 

t  The  lower  values  were  obtained  by  electric  oscillations  of  duration  of  charge  about  0.0006  second.  The  larger 
values  were  obtained  when  duration  of  charge  was  about  0.02  second. 

SMITHSONIAN  TABLES. 


264 


TABLE  276. 
SPECIFIC  INDUCTIVE  CAPACITY  OF  SOLIDS  (AIR  =  UNITY). 


Substance. 

Sp.  ind.  cap. 

Authority. 

Spermaceti        

M 

Sulphur    

2.18 
2.25 
3.84-3.90 
2.88-3.21 

Rossetti. 
Felici. 
Boltzmann. 
Wullner 

« 

2.24 

T   J  Thomson 

M 

2.Q4. 

Blondlot 

« 

2$ 

Trouton  and  Lilly. 

TABLE  277, 


SPECIFIC  INDUCTIVE  CAPACITY  OF  LIQUIDS, 


Substance. 

Sp.  ind.  cap. 

Authority. 

Alcohols  : 
Amyl    .         .         .        . 
Ethyl    .         .         .         .        .  *     .  '     •. 

is-w 

24-27 

32.65 

22.8 

7-5 
1.93-2.45 

2-3 
2.1898 

2.1534 
2.1279 

2.1103 

1.859 

'•934 
1.966 

2.2OI 

2-175 
2.236 

4.6-4.8 
3.07-3.14 
2.25 

3-07 
3.08-3.16 
2.02-2.19 
I.92 
2.2-3.0 

3-!7 
3.02-3.09 

2.15-2.28 

Cohn  and  Arons  :  Tereschin. 

Various. 
Tereschin. 

Various. 

Negreano. 

« 
« 

Landolt  and  Jahn. 

M 

« 

a 
a 
« 

Hopkinson. 
Various. 
Hopkinson. 
Tomaszewski. 
Hopkinson. 
Arons  and  Rubens;   Hopkinson. 
Various. 
Hopkinson. 
Various. 
Hopkinson. 
Hopkinson;  Rosa. 
Various. 
Fuchs. 
Hopkinson. 
Various. 

Methyl          .         .         .        ... 
Propyl           .         .         . 

Benzene  .        . 

average  about    .        .        . 

at  5°  C.      .        .        .  "    .  •      . 
"  15°  C  

"    2S0  C.                                 .... 

"  40°  C  •     . 
Hexane,  between  11°  and  13°  C.     .        . 
Octane,          "       13°.  5-1  4°  C.         .  '      . 
Decane,         "        I3°.5-I4°.2  C.      . 
Amylene,       "        15°-!  6°.  2  C. 
Octylene,       "        n°.5-i3°.6  C.      . 
Decylene,      "        i6°-7  C. 

Oils: 
Arachid         ...... 
Castor  .         .        .        .        . 

Colza    
Lemon  ....                 . 
Neatsfoot      ...                 . 
Olive     ....                 . 
Petroleum    ...                 . 
Petroleum  ether 
Rape-seed     ...                 . 
Sesame          ...                 . 
Sperm           ...                 . 

2.17 
2.13 
2.2—2.4 

2.3-2.6 

SMITHSONIAN  TABLES. 


265 


TABLE  278. 


CONTACT    DIFFERENCE    OF 

Solids  with  Liquids  and 
Temperature  of  substances 


Carbon. 

1 

, 

1 

Platinum. 

C 

H 

J 

N 

.308 

02 

i  6 

(!o?2 

.jw 
.269 

' 

(  -285  ) 

r  alo^ 

Distilled  water  

)  to 

to 

.148 

171 

<     to  / 

177 

<         to 

1% 

.100 

.  l^U 

'*•  I  L 

(  -345) 

•*// 

1 
(+•156 

Alum  solution  :  saturated  [ 
at  16°  c  C.  .                  .    \ 

—.127 

—653 

—•139 

.246 

—225 

-536 

Copper  sulphate  solution  :  ) 
sp.  gr.  1.087  at  i6°.6  C.    f 

- 

.103 

- 

- 

- 

Copper  sulphate  solution  :  1 
saturated  at  is°C.   .     .    J 

- 

.070 

- 

- 

- 

- 

- 

Sea  salt  solution:  sp.  gr.  ) 
1.18  at  2o°5  C.     .    .    .    i 

- 

—475  ^ 

-.605 

- 

—.856 

—•334 

-.565 

Sal-ammoniac      solution  :  ) 
saturated  at  150.5  C.     •    ) 

- 

—396 

-.652 

-.189 

•059 

—364 

-.637 

Zinc  sulphate  solution  :  sp.  1 
gr.  1.125  at  i6°.9  C.  .     .    J 

- 

- 

- 

- 

- 

- 

-.238 

Zinc    sulphate    solution:) 

saturated  at  I5°.3  C.     .    ) 

~ 

*™ 

*" 

*• 

•• 

— 

—43° 

One  part  distilled  water  -f-  ) 

3    parts    saturated    zinc  ? 

— 

— 

— 

_ 

_ 

_ 

—  444 

sulphate  solution  .     .     .    ) 

Strong    sulphuric    acid    in 

distilled  water  : 

i  to  20  by  weight     .     .     . 

- 

- 

- 

_ 

_ 

- 

—•344 

i  to  10  by  volume    .    .    . 

t  about  i 

'  —  -°35  » 

i  to  5  by  weight  .... 

- 

- 

- 

- 

- 

- 

5  to  i  by  weight  .... 

\  to  > 

- 

- 

—  .120 

- 

-•25 

_ 

(3-°) 

Concentrated  sulphuric  acid 

(•55) 
\  to  I 

1.113 

_ 

(     -72 
i     t0 

1-3    ) 

to     [ 

_ 

_ 

Concentrated  nitric  acid 

(-85) 

(  L252 

1.6   ) 

.672 

Mercurous  sulphate  paste  . 

_ 

_ 

_ 

_ 

_ 

_ 

Distilled  water  containing  ) 
trace  of  sulphuric  acid      f 

- 

- 

- 

~ 

- 

- 

—.241 

*  Everett's  "  Units  and  Physical  Constants:  "  Table  of 


SMITHSONIAN  TABLES. 


266 


TABLE  278. 


POTENTIAL    IN     VOLTS. 

Liquids  with  Liquids  in  Air.* 
during  experiment  about  16°  C. 




i 

V    « 

u 

lo 

jo> 

J;J 

IJ 

, 

0° 

fj? 

|3> 

fe 

•81 

1 

I 

to 

1 

1 

n  solution 
irated  at  i 

fl 

8.3 

|? 

"3  i; 

10   M 

ts  « 

Is 

•o  N 

"C  S 

•i 

t 

rt  x 

E.S 

•    1 

1 

Q 

J2  re 

3* 

1* 

l§ 

If 

1 

Mercury   

- 

- 

- 

- 

- 

- 

- 

_ 

- 

_ 

Distilled  water  

.100 

--.I       f\  A  >J 

6 

•^ 

•°43 

4 

Alum  solution  :  saturated 

!    at  i6°5  C  

• 

—.014 

— 

— 

— 

— 

— 

— 

— 

- 

Copper  sulphate  solution  : 
sp.  gr.  1.087  at  i6°.6  C. 

- 

- 

- 

- 

- 

.OCX) 

- 

- 

- 

Copper  sulphate  solution  :  1 
saturated  at  15°  C.   .     .    J 

t 

- 

- 

—•043 

- 

- 

- 

•^95 

.IO2 

- 

Sea  salt  solution  :  sp.  gr.  1 
1.18  at  20°.  5  C.     .     .     .    J 

- 

—•435 

- 

- 

- 

- 

- 

- 

- 

- 

Sal-ammoniac      solution  : 

_     o 

saturated  at  I5°.5  C.      . 

•f 

—•348 

•~ 

— 

~* 

— 

— 

— 

— 

— 

Zinc    sulphate    solution  : 

sp.  gr.  1.125  at  I6°-9  C. 

' 

"" 

Zinc    sulphate     solution  :  J 
saturated  at  1  5°.3  C.     .    J 

-.284 

- 

- 

—  .200 

- 

—.095 

- 

- 

- 

- 

One  part  distilled  water  -f-  ) 

3    parts    saturated    zinc  > 

_ 

_ 

— 

— 

— 

—  .102 

— 

_ 

_ 

_ 

sulphate  solution      .     .    ) 

Strong    sulphuric    acid    in 

distilled  water  : 

i  to  20  by  weight     .     .     . 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

i  to  10  by  volume    .    .    . 

-.358 

- 

- 

- 

- 

- 

- 

- 

- 

- 

i  to  5  by  weight  .... 

.429 

- 

- 

- 

- 

- 

- 

- 

- 

- 

5  to  i  by  weight  .    .    4    . 

- 

—.016 

- 

- 

- 

- 

- 

- 

- 

- 

Concentrated  sulphuric  acid 

.848 

- 

- 

1.298 

1.456 

1.269 

- 

1.699 

- 

- 

Concentrated  nitric  acid 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

Mercurous  sulphate  paste  . 
Distilled  water  containing  1 
trace  of  sulphuric  acid  .    ) 

- 

- 

•475 

- 

- 

- 

- 

- 

- 

.078 

Ayrton  and  Perry's  results,  prepared  by  Ayrton. 
SMITHSONIAN  TABLES. 


267 


TABLE  279. 


CONTACT    DIFFERENCE    OF    POTENTIAL    IN    VOLTS. 

Solids  with  Solids  in  Air.* 
Temperature  of  substances  during  the  experiment  about  18°  C. 


Carbon. 

Copper. 

Iron. 

Lead. 

Platinum. 

Tin. 

Zinc. 

Zinc 
amal- 
gam. 

Brass. 

Carbon  .     .     . 

0 

•370 

485 

.858 

•"3 

•795 

1.096! 

I.2o8t 

•4i4t 

Copper  .    .    . 

—•370 

O 

.146 

•542 

-238 

.456 

•75° 

•894 

.087 

Iron  .... 

-.485t 

—.146 

O 

•401  1 

-.369 

•3'3t 

.6oot 

•744t 

—  .064 

Lead      .     .    . 

—.858 

—•542 

—  401 

0 

—.771 

—.099 

.210 

•357t 

—.472 

Platinum    . 

-.H3t 

.238 

•369 

.771 

o 

.690 

.981 

i.i25t 

.287 

Tin    .... 

—  -795t 

-.458 

—.313 

.099 

-.690 

0 

.281 

•463 

—•372 

Zinc  .... 

—  1.096! 

—•750 

—.600 

-.216 

-.981 

.281 

0 

.144 

—.679 

"    amalgam 

—  i.2o8t 

-.894 

—•744 

-357t 

—  i.i25t 

—•463 

—.144 

o 

—.822 

Brass     .    .     . 

—.414 

—.087 

.064 

.472 

-.287 

•372 

.679 

.822 

0 

The  numbers  not  marked  were  obtained  by  direct  experiment,  those  marked  with  a  dag- 
ger  by  calculation,  on  the  assumption  that  in  a  compound  circuit  of  metals,  all  at  the  same 
temperature,  there  is  no  electromotive  force. 
The  numbers  in  the  same  vertical  column  are  the  differences  of  potential  in  volts  between 
the  substance  named  at  the  top  of  the  column  and  the  substance  named  on  the  same  line  in 
the  first  column,  when  the  two  substances  are  in  contact. 

The  metals  used  were  those  ordinarily  obtained  in  commerce. 

*  Everett's  "  Units  and  Physical  Constants."    The  table  is  from  Ayrton  and  Perry's  experiments,  and  was  pre- 
pared by  Ayrton. 

SMITHSONIAN  TABLES. 

268 


TABLE  280. 

DIFFERENCE    OF    POTENTIAL    BETWEEN    METALS    IN    SOLUTIONS    OF 

SALTS. 


The  following  numbers  are  given  by  G.  Magnanini  *  for  the  difference  of  potential  in  hundredths  of  a  volt  between 
zinc  in  a  normal  solution  of  sulphuric  acid  and  the  metals  named  at  the  head  of  the  different  columns  when  placed 
in  the  solution  named  in  the  first  column.  The  solutions  were  contained  in  a  U-tube,  and  the  sign  of  the  differ- 
ence of  potential  is  such  that  the  current  will  flow  from  the  more  positive  to  the  less  positive  through  the  ex- 
ternal circuit. 


Strength  of  the  solution  in 
gramme   molecules  per 
litre. 

Zinc.t 

Cadmium.f 

Lead. 

Tin. 

Copper. 

Silver. 

No.  of 
molecules. 

Salt. 

Difference  of  potential  in  centivolts. 

°-5 

H2SO4 

0.0 

36.6 

Sl-3 

5J-3 

100.7 

I2I-3 

I.O 

NaOH 

—32.1 

'9-5 

31.8 

0.2 

80.2 

95-8 

1.0 

KOH 

—42.5 

'5-5 

32.0 

—  1.2 

77.0 

104.0 

°-5 

Na2SO4 

1.4 

35-6 

50-8 

5*-4 

IOI.1 

120.9 

I.O 

Na2S2O8 

—5-9 

24.1 

45-3 

45-7 

38.8 

64.8 

I.O 

KNO3 

ii.Sj 

3*-9 

42.6 

3i-i 

8l.2 

105.7 

I.O 

NaNO3 

"•5 

32-3 

51.0 

40.9 

95-7 

114.8 

o-S 
°-5 

K2CrO4 
K2Cr2O7 

23-9J 

72.8 

42.8 
61.1 

41.2 

78.4 

£2 

94.6 
123.6 

I2I.O 

I324 

o-5 

K2S04 

1.8 

347 

51.0 

40.9 

95-7 

II4.8 

°-5 

(NH4)2S04 

—o-S 

37-i 

53-2 

57-6J 

101.5 

125-7 

0.25 

K4FeC6N6 

—6.1 

33-6 

50-7 

41.2 

—  t 

87.8 

0.167 

K6Fe2(CN)2 

4I.O§ 

80.8 

81.2 

130.9 

110.7 

124.9 

I.O 

KCNS 

—  1.2 

32-5 

52.8 

527 

52-5 

72.5 

I.O 

NaNO3 

4-5 

35-2 

50.2 

49.0 

103.6 

104.6? 

o-5 
0.125 

I.O 

SrNO3 
Ba(NO3)2 
KN03 

14.8 
21.9 

38-3 
39-3 
35-6 

50.6 
5I-7 
47-5 

48.7 
52.8 
49-9 

103.0 
109.6 
104.8 

"9-3 
121.5 
115.0 

O.2 

KC1O« 

i5-ict 

39-9 

53-8 

57-7 

105-3 

120.9 

0.167 

ItBrOs 

13-20! 

40.7 

S«'3 

50-9 

111.3 

120.8 

I.O 

NH4C1 

2.9 

32-4 

Si-3 

50.9 

81.2 

101.7 

I.O 

KF 

2.8 

22.5 

41.1 

50.8 

61.3 

61.5 

I.O 

NaCl 

— 

3T-9 

51.2 

50-3 

80.9 

101.3 

I.O 
I.O 

KBr 
KC1 

2-3 

y-7 

32.1 

47.2 
51.6 

52-5 
52-6 

736 
81.6 

82.4 

107.6 

0.5 

NaaSOg 

—8.2 

28.7 

41.0 

31.0 

68.7 

103.7 

-II 

NaOBr 

!8.4 

4i.6 

73-1 

70.6  1 

89.9 

99-7 

I.O 

C4H606 

5-5 

39-7 

61.3 

54-4§ 

104.6 

123.4 

°-5 

C4H606 

4.1 

41-3 

61.6 

57.6 

110.9 

125.7 

0-5 

C4H4KNa06 

—7-9 

3i-5 

5T-5 

42-47 

100.8 

119.7 

1890. 


*  "  Rend,  della  R.  Ace.  di  Roma," 

t  Amalgamated. 

t  Not  constant. 

S  Aiter  some  time. 

||  A  quantity  of  bromine  was  used  corresponding  to  NaOH  =  i. 


SMITHSONIAN  TABLES. 


269 


TABLE  281 . 


VARIATION    OF    ELECTRICAL    RESISTANCE    OF   CLASS  AND    PORCELAIN 

WITH    TEMPERATURE. 

The  following  table  gives  the  values  of  a,  b,  and  c  in  the  equation 

log  R  —  a  -f  bt  +  cP, 

where  R  is  the  specific  resistance  expressed  in  ohms,  that  is,  the  resistance  in  ohms  per  centimetre  of  a  rod  on& 
square  centimetre  in  cross  section.* 


No. 
I 

Kind  of  glass. 

Density. 

a 

b 

c 

Range  of 

temp. 
Centigrade. 

Test-tube  glass           .... 

- 

13.86 

—.044 

.000065 

0°-250° 

2 

«       «         « 

2.458 

14.24 

—•°55 

.0001 

37-IjI 

3 

Bohemian  glass          . 

2-43 

1  6.2  1 

—-043 

.0000394 

60-174 

4 

Lime  glass  (Japanese  manufacture)  . 

2-55 

U-H 

—.031 

—  .000021 

10-85 

5 

« 

2.499 

14.002 

—.025 

—  .00006 

35-95 

6 

Soda-lime  glass  (French  flask) 

2-533 

14.58 

—.049 

.000075 

45-120 

7 

Potash-soda  lime  glass 

2.58 

16.34 

-.0425 

.0000364 

66-193 

8 

Arsenic  enamel  flint  glass 

3-07 

18.17 

—•055 

.000088 

105-135 

9 

Flint  glass  (Thomson's  electrometer 
jar)         

3-I72 

18.021 

—  -036 

—  .0000091 

100-200 

10 

Porcelain  (white  evaporating  dish)  . 

- 

15-65 

—.042 

.00005 

68-290 

COMPOSITION  OF  SOME  OF  THE  ABOVE  SP  CIMENS  OF  GLASS. 

Number  of  specimen  =r 

3 

4 

5 

7 

8               9 

Sil 
Po 
So 
Le 

ca      
tash    

61.3 
22.9 
Lime,  etc. 
by  diff. 

57-2 

21.  1 

Lime,  etc. 
by  diff. 

70.05 
1.44 
14.32 
2.70 

75-65 
7-92 
6.92 

54.2          55.18 
10.5          13.28 
7.0 
23.9         31.01 

da               .        .        .    •     .''• 

id  oxide     .... 

Lime       

15.8 

16.7 

!°-33 

8.48 

o-3          0.35 

Magnesia        .... 

- 

- 

- 

0.36 

0.2               0.06 

Arsenic  oxide          .        .«.  .  .    .  ; 

. 

- 

- 

- 

3-5 

Alumina,  iron  oxide,  etc. 

- 

- 

i-45 

0.70 

0.4          0.67 

SMITHSONIAN  TABLES. 


*  T.  Gray,  "Phil.  Mag."  1880,  and  "  Proc.  Roy.  Soc."  1882. 


270 


TABLE  282, 
RELATION   BETWEEN  THERMAL  AND   ELECTRICAL  CONDUCTIVITIES. 


That  there  is  a  close  relation 
between  the  thermal  and  the 
electrical  conductivities  of 
metal  \\as  shown  experimen- 
tally by  Wiedemann  and  Franz 
in  1853,  and  had  been  referred 
to  by  Forbes,  with  whom  a 
difficulty  arose  with  regard  to 
the  direction  of  the  variation 
with  temperature.  The  ex- 
periments of  Tail  and  his  stu- 
dents have  shown  that  this 
difficulty  was  largely,  if  not 
entirely,  due  to  experimental 
error.  The  same  relation  has 
been  shown  to  hold  for  alloys 
by  Chandler  Roberts  and  by 
Neumann.  This  relation  was 


a.  VALUES  IN  ARBITRARY  UNITS  AT  15°  C. 


Substance. 

lis 

*M 

/16 

Lead      .     . 

7.93 

4.569 

1.74 

Tin    ... 

14.46 

8.823 

1.64 

Zinc  .    .     . 

25-45 

14.83 

1.72 

Copper  .     . 
Iron,  No.  I 

41.52 
14.18 

24.04 
6.803 

2.08 

"           "       2 

9.64 

4.060 

2-37 

"       "    3 

13.75 

6.565 

2.09 

denied  by  H.  F.  Weber,  and 
has  been  again  experimentally 
investigated  and  apparently 
established  by  the  experiments 
of  Kirchhoff  and  Hansemann, 
of  L.  Lorenz,  of  F.  Kohl- 
rausch,  and  of  Berget. 

Putting  l=i  thermal  conduc- 
tivity, and  k  —  electrical  con- 
ductivity, Kirchhoff  and 
Hansemann  find  the  values  in 
Table  a.  This  table  shows 
iron  to  deviate  considerably 
from  the  other  metals  in  the 
relationship  of  the  two  con- 
ductivities ;  but  this  may  possi- 
bly be  explained  by  its  mag- 
netic properties. 


Lorenz's  results  *  show  that  the  ratio  //  k  for  the  different  metals,  except  iron,  is  nearly  constant  for  values 
at  o°  and  100°  C.,  but  that  the  ratio  is  generally  greater  for  poorly  conducting  substances.     He  shows  that  the 

ratio  lT^"~i~~^~  remains  nearly  constant  for  all  metals  examined,  with  the  exception  of  iron,  and  has  an  aver- 
age value,  as  shown  by  Table  to,  of  about  1.37.  He  concludes  that  I / k—  constant  X  7",  where  T  is  the  abso- 
lute temperature. 

In  this  table  the  values  of  /  and  k  are  given  in  c.  g.  s.  units,  and  the  metals  are  arranged  in  the  order  of 
their  heat  conductivities.     The  same  specimens  were  used  for  both  the  thermal  and  the  electrical  experiments. 

to.  VALUES  IN  C.  G.  S.  UNITS. 


Substances. 

/o 

/1  00 

*0XioS 

*i  ooXio" 

k 

*o 

A.o        /. 

*1.0      '    *0 

Copper      .        .        .~      « 

0.7198 

0.7226 

45-74 

33-82 

1574 

I-358 

Magnesium 

0.3760 

0.3700 

24-47 

17-5° 

»537 

I-398 

Aluminium 
Brass,  red. 

0-3435 
0.2460 

0.3619 
0.2827 

22.46 
15-75 

I7-3I 
I3-3I 

'529 

1562 

1.367 
1.360 

Cadmium  .         .        .        .    \ 
Brass,  yellow     .         .         . 

O.22OO 
O.2O4I 

0.2045 
0.2540 

14.41 
12.62 

10.18 

11.00 

1527 

1617 

L3I5 

1.428 

0.1665 

0.1627 

10.^7 

6.628 

i6oc 

I.C-JQ 

Tin    

0.1528 

0.1423 

9-346 

6.524 

iWVJ 

1635 

1-334 

Lead  

0.0836 

0.0764 

5.141 

7.602 

1627 

I.  7O4. 

German  silver  .        .        • 

O.O7OO 

0.0887 

3.766 

3-632 

1858 

I-3M 

Antimony  .         .         .        • 

0.0442 

0.0396 

2.199 

1.522 

2OII 

1.294 

Bismuth     .... 

0.0177 

O.OT64 

0.929 

0.633 

1900 

1.372 

C.  BERGET'S  EXPERIMENTS.! 

The  same  specimens  were  used  for  both  experiments.     It  will  be  seen  that  the  ratio  is  nearly  constant,  but  not 

exactly  so. 


Substance. 

/ 

k  X  10-5 

1- 

Substance. 

/ 

/feXio-6 

^ 

Copper  .     .     . 
Zinc  .... 

1.0405 
0-303 

6^.13 

18.00 

1.6 
1-7 

Tin  .... 
Lead    .     .     . 

0.151 
0.08  1  o 

8.33 

5.06 

1.8 
1.6 

Brass     .     .     . 
Iron  .... 

0.2625 
0.1587 

15-47 
9.41 

i«7 
«-7 

Antimony 
Mercury    .     . 

0.042 

0.0201 

2.47 
1.  06 

;i 

d.  KOHLRAUSCH'S  RESULTS. 

An  interesting  confirmation  of  the  relationship  of  the  two  conductivities  has  been  furnished  by  F.  Kohl- 
rausch,  who  has  shown  that  tempering  steel  causes  equal  proportional  changes  in  the  thermal  and  electncal 
conductivities  of  the  metal,  thus  leaving  the  ratio  l/k  unchanged  by  the  process.} 


Tempered  steel 
Soft  steel 


/=  0.062  ;  £  =  3.3  5  //*  =  0.019 
"  =  o.iu;  "  =5-5*   " 


In  the  consideration  of  this  subject  it  must  be  borne  in  mind  that  closely  accurate  values  of  thermal  conduc- 
tivity are  very  difficult  to  obtain,  and  hence  fairly  large  variations  are  to  be  expected. 


*  "  Wied.  Ann."  vol.  13,  p.  508. 
t  "  Compt.  Rend."  vol.  no,  p.  76. 

SMITHSONIAN   TABLES. 


/  is  in  c.  g.  s.  units  and  k  in  terms  of  mercury. 


271 


TABLE  283. 
ELECTROCHEMICAL  EQUIVALENTS  AND  INTERNATIONAL  ATOMIC  WEIGHTS. 


With  the  exception  of  the  value  given  for  silver  and  that  corresponding  to  valence  2  for  copper,  the  electrochemical 
equivalents  given  in  this  table  have  been  calculated  from  the  atomic  weig 


hts  and  one  or  two  of  the  more  com- 


mon apparent  valences  of  the  substance.  The  value  given  for  silver  is  that  which  was  adopted  by  the  Inter- 
national Congress  of  Electricians  at  Chicago  in  1894.  The  number  for  silver  is  made  the  basis  of  the  table  ;  the 
other  numbers,  with  the  exception  of  copper,  above  referred  to,  are  theoretical. 

The  International  Atomic  Weights  are  quoted  from  the  report  of  the  International  Committee  on  Atomic  Weights 
("Jour.  Am.  Chem.  Soc.,"  vol.  25,  p.  4). 


Substance. 

Symbol. 

Relative 
atomic  wt. 
Oxygen  =  16. 

Relative 
atomic  wt. 
Hydrogen  =  i. 

Valence. 

Electrochemical 
equivalent  in  grammes 
per  coulomb  X  1000. 

Aluminum    .         .         ;  , 

Al 

27.1 

26.9 

3 

.0936 

Antimony     .         ;         ; 

Sb 

120.2 

H9.3 

3 

.4150 

it 

" 

" 

" 

5 

.2490 

Argon  .... 

A 

39-9 

39-6 

Arsenic         .         .         .  • 

As 

75-0 

74-4 

3 

.2590 

•; 

<< 

« 

«< 

5 

.1554 

Barium 

Ba 

137-4 

136.4 

2 

.7116 

Bismuth 

Bi 

208.5 

206.9 

3 

.7199 

i< 

ii 

" 

'* 

5 

.4319 

Boron  .... 

B 

II. 

10.9 

3 

.0380 

Bromine 

Br 

79.96 

79.36 

i 

.8283 

Cadmium 

Cd 

II2.4 

in.  6 

2 

.5822 

Caesium 

Cs 

133. 

132. 

I 

1.3777 

Calcium 

Ca 

40.1 

39-8 

2 

•  2077 

Carbon 

C 

12.0 

11.91 

4 

.0311 

Cerium 

Ce 

140. 

139. 

2 

.7251 

Chlorine 

Cl 

35-45 

35.18 

I 

.3672 

Chromium    .         .         ; 

Cr 

52.1 

5f;7 

3 

.1800 

"            .         •         . 

c« 

ii 

6 

.0900 

Cobalt 

Co 

59-0 

58.56 

2 

-3056 

"      •         . 

(C 

« 

« 

3 

.2038 

Columbium  .         .         . 

Cb 

94. 

93-3 

5 

.1947 

Copper 

Cu 

63.6 

63.1 

I 

.6588 

•         •         . 

ii 

44 

" 

2 

.3290 

Erbium 

Er 

166. 

164.8 

2 

.8598 

Fluorine       .         .         . 

F 

19. 

18.9 

I 

.1968 

Gadolinium  . 

Gd 

156. 

155. 





Gallium        .         . 

Ga 

70. 

69.5 

3 

.2417 

Germanium  . 

Ge 

72.5 

71.9 

Glucinum     .         .         i 

Gl 

9.1 

9.03 

2 

.0471 

Gold     .... 

Au 

197.2 

195-7 

3 

.6809 

Helium 

He 

4- 

4- 



Hydrogen     . 

H 

1.008 

1.  000 

i 

.0104 

Indium 

In 

114. 

113.1 

3 

.3936 

Iodine  .... 

I 

126.85 

125.90 

I 

I.3HO 

Indium 

Ir 

193.0 

I9I-5 

4 

.4998 

Iron      .... 

Fe 

55.9 

55-5 

2 

.2895 

"        •         •         • 

" 

" 

t  < 

3 

.1930 

Krypton 

Kr 

81.8 

81.2 

Lanthanum  . 

La 

138.9 

137.9 

2 

.7194 

Lead    .... 

Pb 

206.9 

205.35 

2 

1.0716 

Lithium 
Magnesium  . 

Li 

Mg 

7.03 
24.36 

6.98 
24.18 

I 
2 

.0728 
.1262 

Manganese  . 

Mn 

55-0 

54.6 

2 

.2849 

... 

ii 

4 

.1424 

SMITHSONIAN  TALES. 


2/2 


TABLE  283. 
ELECTROCHEMICAL  EQUIVALENTS  AND  INTERNATIONAL  ATOMIC  WEIGHTS. 


Substance. 

| 

Symbol. 

Relative 
atomic  wt. 
Oxygen  =  16. 

Relative 
atomic  wt. 
Hydrogen  =  i. 

Valence. 

Electrochemical 
equivalent  in  grammes 
per  coulomb  X  1000 

Mercury 

Hg 

2OO.O 

198.5 

I 

2.0717 

Molybdenum 
Neodymium          . 

Mo 

Nd 

96.0 
143-6 

95-3 
142.5 

2 

6 

1-0359 
.1657 

Neon    .... 

Ne 

20. 

19.9 

— 



Nickel  . 

Ni 

cfi  7 

-Q    „ 

50.7 

58-3 

2 

.3040 

Nitrogen 

N 

1  1 

14.04 

13-93 

3 
3 

.2027 
.0485 

Osmium 

Os 

191. 

189.6 

5 
6 

.0291 
.3297 

Oxygen 
Palladium     . 

0 

Pd 

16.00 
106.5 

15.88 
105-7 

2 
2 

.0829 
.5516 

•                   •                  • 

*  4 

4  * 

4  * 

5 

.22O6 

Phosphorous 

P 

31-0 

30.77 

3 

.1070 

. 

5 

.0642 

Platinum 

Pt 

194.8 

193-3 

2 

1.0098 

•                  •                   • 

4  * 

4  * 

4 

.5040 

Potassium     . 
Praesodymium 

K 
Pr 

39-15 
140.5 

38.86 
139-4 

i 

*  *Jvlr:7 
.4055 

Radium 

Rd 

225. 

223.3 

— 



Rhodium 
Rubidium     .         . 

Rh 
Rb 

103.0 

85-4 

102.2 

84.8 

3 

i 

.3556 

.8846 

Ruthenium  . 

Ru 

101.7 

lOO.g 

4 

.2634 

Samarium     .         .         . 

Sm 

150. 

148.9 

Scandium 

Sc 

44.1 

43.8 

— 



Selenium 

Se 

79.2 

78.6 

2 

.4102 

Silicon 

Si 

28.4 

28.2 

4 

•0735 

Silver  .... 

Ag 

107-93 

107.12 

i 

I.IlSO 

Sodium 

Na 

23-05 

22.88 

i 

.2388 

Strontium     . 

Sr 

87.6 

86.94 

2 

•4537 

Sulphur         ... 

S 

32.06 

31.83 

2 

.1660 

Tantalum     . 

Ta 

183. 

181.6 

5 

.3791 

Tellurium     . 

Te 

127.6 

126.6 

2 

.6609 

Terbium 

Tb 

160. 

158.8 





Thallium      . 

Tl 

204.1 

202.6 

I 

2.1142 

Thorium 

Th 

232.5 

230.8 

2 

1.2042 

Thulium 

Tm 

171. 

169.7 

— 



Tin       . 

Sn 

119.0 

IlS.l 

2 

.6163 

"         .         •         .         • 

" 

" 

44 

4 

.3082 

Titanium      .         . 

Ti 

48.1 

47-7 

4 

.1246 

Tungsten 

W 

184. 

182.6 

6 

.3177 

Urnaium       .         .         . 

u 

238.5 

236.7 

2 

1-2353 

"              •         •         • 

44 

44 

44 

3 

.8235 

Vanadium     .         . 

V 

51.2 

50.8 

3 

.1768 

it 
.         .         • 

" 

fi 

5 

.1061 

Xenon  .... 

Xe 

128. 

127. 





Ytterbium     .         .         . 

Yb 

173.0 

I7I.7 

— 



Yttrium 

Yt 

89.0 

88.3 

2 

.4610 

Zinc      .... 

Zn 

65-4 

64.9 

2 

.3387 

Zirconium     . 

Zr 

90.6 

89.9 

4 

.2346 

SMITHSONIAN  TABLES. 


273 


TABLES  284,  285. 

PERMEABILITY  OF  IRON. 

TABLE  284.— Permeability  of  Iron  Rings  and  Wire. 

This  table  gives,  for  a  few  specimens  of  iron,  the  magnetic  induction  B,  and  permeability  /u.,  corresponding  to  the 
magneto-motive  forces  H  recorded  in  the  first  column.  The  first  specimen  is  taken  from  a  paper  by  Rowland,* 
and  refers  to  a  welded  and  annealed  ring  of  "Burden's  Best"  wrought  iron.  The  ring  was  6.77  cms.  in  mean 
diameter,  and  the  bar  had  a  cross  sectional  area  of  0.916  sq.  cms.  Specimens  2-4  are  taken  from  a  paper  by 
Bosanquet,t  and  also  refers  to  soft  iron  rings.  The  mean  diameters  were  21.5,  22.1,  and  22.725  cms.,  and  the 
thickness  of  the  bars  2.535,  1.295,  and  .7544  cms.  respectively.  These  experiments  were  intended  to  illustrate  the 
effect  of  thickness  of  bar  on  the  induction.  Specimen  5  is  from  Ewing's  book,J  and  refers  to  one  of  his  own 
experiments  on  a  soft  iron  wire  .077  cms.  diameter  and  30.5  cms.  long. 


Specimen  1 

2 

3 

4 

6 

•&£.*! 

B 

* 

B 

* 

B 

M 

B 

V- 

B 

* 

£.0  11!  s 

0.2 

80 

400 

126 

630 

6S 

325 

8S 

42S 

22 

no 

tfg.:l 

o*5 

33° 

660 

377 

754 

224 

448 

214 

428 

74 

148 

I  c  c  e.S 

I.O 

145° 

1450 

1449 

1449 

840 

840 

885 

246 

246 

<u  5'K  £3 

2.0 

4840 
9880 

2420 

1976 

4564 
9900 

2282 
1980 

3533 
8293 

1766 
'659 

2417 
8884 

1777 

950 
12430 

2486 

7i|g| 

1  0.0 

12970 

1297 

13023 

1302 

12540 

1254 

11388 

"39 

15020 

1502 

M'O^JJ:  c 

2O.O 

14740 

737 

14911 

746 

14710 

735 

13273 

664 

15790 

789 

o  4>U  c'~ 

5O.O 

16390 

328 

16217 

324 

16062 

321 

13890 

278 

^^•g^.h 

1  00.0 

17148 

171 

17900 

179 

14837 

148 

TABLE  285. -Permeability  of  Transformer  Iron.§ 


This  table  contains  the  results  of  some  experiments  on  transformers  of  the  Westinghouse  and  Thomson-Houston 
types.  Referring  to  the  headings  of  the  different  columns,  Mis  the  total  magneto-motive  force  applied  to  the  iron ; 
M / 1  the  magneto-motive  force  per  centimetre  length  of  the  iron  circuit :  B  the  total  induction  through  the  mag- 
netizing coil ;  B  /a  the  induction  per  square  centimetre  of  the  mean  section  of  the  iron  core  ;  M  /  B  the  magnetic 
reluctance  of  the  iron  circuit;  El/Ma  the  permeability  of  the  iron,  a  being  taken  as  the  mean  cross  section  of  the 
iron  circuit  as  it  exists  in  the  transformer,  which  is  thus  slightly  greater  than  the  actual  cross  section  of  the  iron. 


(a)  WESTINGHOUSE  No.  8  TRANSFORMERS  (ABOUT  2500  WATTS  CAPACITY). 

First  specimen. 

Second  specimen. 

M 

T 

B 

M 

Bl 

B 

M 

Bl 

B 

a 

B 

Ma 

B 

a 

Ma 

20 

0-597 

2I8XI03 

1406 

0.917  X  io~4 

2360 

16X10* 

1032 

1.25X10-* 

1730 

40 

1.194 

587        " 

3790 

0.681         " 

3120 

49      " 

3140 

0.82 

2640 

60 

1.791 

878        - 

5660 

0.683        " 

3180 

82      « 

5290 

0.73      " 

2970 

80 

2.338 

1091 

7040 

0-734        " 

2960 

104      " 

6710 

0-77       « 

2820 

100 

2-985 

1219        " 

7860 

0.819        " 

2640 

118      " 

76lO 

0.85      " 

2560 

1  20 

3.582 

1330 

8580 

0.903        " 

2410 

124      " 

8000 

0.97       " 

2250 

140 
160 

4.179 
4.776 

1405        " 

M75        " 

9060 
9510 

0.994 
1.090        " 

2186 
20OO 

135      " 

8450 
8710 

1.07 
1.18      " 

2036 
l830 

1  80 

5-373 

1532        " 

9880 

I.lSo        " 

1850 

140      " 

9030 

1.29      « 

1690 

200 

5-970 

1581 

IO2OO 

1.270        " 

I72O 

142      " 

9160 

1.41       " 

1540 

220 

6.567 

1618      " 

10430 

1.360        " 

1590 

144 

9290 

1410 

260 

7.761 

1692      " 

IO9IO 

1.540 

1410 

; 

" 

" 

SMITHSONIAN  TABLES. 


*  "  Phil.  Mag.''  4th  series,  vol.  xlv.  p.  151. 

t  Ibid,  sth  series,  vol.  xix.  p.  73. 

$  "  Magnetic  Induction  in  Iron  and  Other  Metals.' 

§  T.  Gray,  from  special  experiments. 


274 


TABLE  285, 


PERMEABILITY    OF    TRANSFORMER    IRON. 


(b)  WESTINGHOUSE  No.  6  TRANSFORMERS  (ABOUT  1800  WATTS  CAPACITY). 

First  specimen. 

Second  specimen. 

M 

T 

B 

M 

Bl 

B 

M 

Bl 

B 

a 

£ 

Ma 

B 

a 

£ 

Ma 

2O 

0.62 

I47XI03 

1320 

I.36XIO-4 

2140 

2I5XI03 

1940 

0.93XIO-4 

3HO 

40 
60 

1.23 
i.8S 

442     " 
697 

3980 
6280 

0.91      " 

0.86    " 

3260 

339° 

615     " 
826     " 

5540 
7440 

0.64      " 
0.72      " 

4490 
4030 

80 

2.46 

862 

7770 

0.93    " 

3r4Q 

986     " 

8880 

0.8  1     " 

3590 

100 

3.08 

949 

8550 

1.05    « 

2770 

1050     " 

9460 

0.95     « 

3060 

120 

3-70 

1010 

9106 

1.19    « 

2450 

IIOO     " 

9910 

1.09     " 

2670 

140 

4-3  i 

1060 

955° 

i-33     ' 

22IO 

1140    " 

10300 

1.23 

2430 

1  60 

4-93 

1090    " 

9820 

1.47     " 

1990 

1170  " 

lOfOO 

1-37     " 

2l8o 

1  80 

5-5.S 

1  120     " 

IOIOO 

1.61     " 

1830 

1190  " 

10700 

1.51     " 

1970 

200 

6.16 

1150     « 

10400 

1.74    « 

1680 

•* 

~ 

•• 

~ 

(C)  WESTINGHOUSE  No.  4  TRANSFORMER 
(ABOUT  1200  WATTS  CAPACITY). 

(d)  THOMSON-HOUSTON  1500  WATTS  TRANSFORMER. 

M 

B                  M 

Bl 

M 

B 

M 

Bl 

M 

I 

B 

a 

B 

Ma 

M 

T 

B 

a 

-B 

Ma 

20 

0.69 

i47Xio8 

1470 

1.  36XIO-4 

2140 

20 

0.42 

7oXio8 

1560 

2.86X10-4 

3730 

40 

0.84 

142    " 

3160 

2.81     " 

37»o 

40 

1.38 

406    « 

4066 

0.98 

' 

2940 

60 

1.26 

214 

4770 

2.8  1       " 

379^ 

80 

1.68 

265 

5910 

3.02  « 

3520 

60 

2.07 

573    " 

5730 

1.05      « 

2770 

100 

2.10 

309 

6890 

3.24  " 

3280 

120 

2.52 

348 

7760 

345    " 

3080 

80 

2.76 

659    « 

6590 

1.  21 

1 

2390 

160 

3-^6 

408 

9IOO 

3.92    ' 

2710 

200 

4.20 

456 

10200 

4-39    " 

2430 

100 

34.S 

714    " 

7140 

1.40 

2070 

240 

5-04 

495 

1  1000 

4.87     « 

2190 

1  20 

4.14 

748    « 

749° 

1.  60 

t 

1810 

280 
320 

5.88 
6.72 

524 
55° 

11690 
I227O 

5-35    " 
5.82    « 

1990 
1820 

360 

7-S6 

573 

12780 

6.29    " 

1690 

140 

4-83 

777    " 

7770 

I  JO 

i 

1610 

400 

8.40 

59i     " 

13180 

6.78     " 

1570 

440 

9.24 

504    " 

13470 

7.28    « 

1460 

275 


TABLE  286. 


COMPOSITION    AND    MAGNETIC 


This  table  and  Table  289  below  are  taken  from  a  paper  by  Dr.  Hopkinson  *  on  the  magnetic  properties  of  iron  and  steel. 
which  is  stated  in  the  paper  to  have  been  240.  The  maximum  magnetization  is  not  tabulated  ;  but  as  stated  in  the 
by  47T.  "  Coercive  force  "  is  the  magnetizing  force  required  to  reduce  the  magnetization  to  zero.  The  '*  demagr 
previous  magnetization  in  the  opposite  direction  to  the  "  maximum  induction  "  stated  in  the  table.  The  "  energy 
which,  however,  was  only  found  to  agree  roughly  with  the  results  of  experiment. 


No. 
of 
Test 

Description  of 
specimen. 

Temper. 

Chemical  analysis. 

Total 
Carbon 

Manga 
nese. 

Sulphur. 

Silicon 

Phos- 
phorus. 

Other 
substances. 

I 

Wrought  iron    . 

Annealed 

_ 

_ 

_ 

_ 

_ 

2 

Malleable  cast  iron    . 

" 

- 

— 

— 

_ 

_ 

_ 

3 

Gray  cast  iron  . 

_ 

- 

- 

- 

_ 

_ 

_ 

4 

Bessemer  steel  . 

- 

0.045 

O.2OO 

0.030 

None. 

0.040 

_ 

Whitworth  mild  steel 

Annealed 

0.090 

0.153 

0.016 

" 

0.042 

- 

6 

"                " 

" 

0.320 

0.438 

0.017 

0.042 

0-035 

— 

u                       « 

(  Oil-hard- 

u 

M 

(l 

(( 

7 

(    ened 

~ 

8 

"              " 

Annealed 

0.890 

O.l65 

0.005 

0.081 

0.019 

- 

(  Oil-hard- 

9 

• 

|    ened 

— 

10 

Hadfield's  manganese  ) 
steel                            J    ' 

- 

1.005 

12.360 

0.038 

0.204 

0.070 

- 

ii 

Manganese  steel 

As  forged 

0.674 

4-73° 

0.023 

0.608 

0.078 

_ 

12 

"            " 

Annealed 

" 

" 

" 

u 

" 

— 

«            it 

(  Oil-hard- 

u 

<4 

(l 

u 

*3 

*        * 

{    ened 

14 

if            « 

As  forged 

1.298 

8.740 

0.024 

0.094 

0.072 

_ 

15 

"            " 

Annealed 

« 

it 

16 

"       j    .    •'.  ., 

{  Oil-hard- 
|    ened 

« 

« 

u 

« 

a 

~ 

17 

Silicon  steel 

As  forged 

0.685 

0.694 

? 

3-438 

0.123 

.. 

18 

u              « 

Annealed 

" 

" 

" 

« 

_ 

«(           « 

(  Oil-hard- 

t( 

l( 

H 

(( 

u 

I9 

... 

|    ened 

20 

Chrome  steel     . 

As  forged 

0.532 

0-393 

0.020 

O.22O 

O.O4I 

0.621  Cr. 

21 

"         "       .        ... 

Annealed 

" 

" 

M 

« 

< 

(  Oil-hard- 

(( 

<4 

22 

'  • 

|    ened 

' 

" 

23 

24 

«             « 

As  forged 
Annealed 

0.687 

M 

0.028 

" 

0.134 

0.043 

1.195  Cr. 

{< 

(  Oil-hard- 

<{ 

25 

. 

(    ened 

" 

" 

" 

li 

26 

Tungsten  steel  .        . 

As  forged 

1-357 

0.036 

None. 

0.043 

0.047 

4.649  W. 

27 

"            "... 

Annealed 

" 

« 

" 

" 

" 

(  Hardened 

28 

"            "... 

^    in  cold 

* 

u 

« 

« 

« 

u 

(    water 

t  Hardened 

29 

"            "     . 

|    in  tepid 

H 

11 

" 

M 

« 

* 

(    water 

30 

"    (French)   . 

(  Oil-hard- 
(    ened 

0.5II 

0.625 

None. 

0.021 

0.028 

3-444  W. 

31 

"            "... 

Very  hard 

0.855 

0.312 

- 

O.I5I 

0.089 

2-353  w- 

32 

Gray  cast  iron   . 

— 

3-455 

0.173 

0.042 

2.044 

O.I5I 

2.064  C.t 

33 

Mottled  cast  iron 

— 

2.581 

0.610 

0.105 

1.476 

o-435 

1.477  C.t 

34 

35 

White       "                  . 
Spiegeleisen 

- 

2.036 
4.510 

0.386 
7.970 

0.467 
Trace. 

0.764 
0.502 

0.458 
0.128 

*  Phil.  Trans.  Roy.  Soc.  vol.  176. 
SMITHSONIAN  TABLES. 


t  Graphitic  carbon. 


2/6 


TABLE  286. 


PROPERTIES   OF   IRON    AND   STEEL. 


The  numbers  in  the  columns  headed  "  magnetic  properties  "  give  the  results  for  the  highest  magnetizing  force  used, 
paper,  it  may  be  obtained  by  subtracting  the  magnetizing  force  (240)  from  the  maximum  induction  and  then  dividing 
netizing  force  ;'  is  the  magnetizing  force  which  had  to  be  applied  in  order  to  leave  no  residual  magnetization  after 
dissipated"  was  calculated  from  the  formula: — Energy  dissipated  =:  coercive  force  X  maximum  induction  -f-  IF 


No. 
of 
Test. 

Description  of 
specimen. 

Temper. 

Specific 
electri- 
cal resis- 
tance. 

Magnetic  properties. 

Energy  dis- 
sipated per 
cycle. 

Maxi- 
mum in- 
duction. 

Residual 
induc- 
tion. 

Coer- 
cive 
force. 

Demag- 
netizive 
force. 

I 

Wrought  iron   . 

Annealed 

.01378 

18251 

7248 

2.30 

_ 

13356 

2 

Malleable  cast  iron  . 

" 

•03254 

12408 

7479 

8.80 

— 

34742 

3 

Gray  cast  iron  . 

— 

.10560 

10783 

3928 

3-80 

— 

13037 

4 

Bessemer  steel  . 

— 

.01050 

18196 

7860 

2.96 

— 

I7I37 

5 

Whitworth  mild  steel 

Annealed 

.01080 

19840 

7080 

1.63 

_ 

10289 

6 

"                « 

" 

.01446 

18736 

9840 

6-73 

- 

40120 

7 

" 

(  Oil-hard- 
l    ened 

.01390 

18796 

11040 

II.OO 

- 

65786 

8 

"                " 

Annealed 

•01559 

l6l20 

10740 

8.26 

- 

42366 

9 

"                " 

(  Oil-hard- 
(    ened 

•01695 

l6l2O 

8736 

I9.38 

- 

99401 

10 

Hadfield's   manganese  ) 
steel                             }  ' 

- 

.06554 

3IO 

- 

- 

- 

ii 

Manganese  steel 

As  forged 

.05368 

4623 

2202 

23-50 

37-13 

34567 

12 

"            " 

Annealed 

.03928 

10578 

5848 

33-86 

46.10 

113963 

(  Oil  harrl 

13 

. 

\  \_-Mi-narQ- 
I    ened 

•05556 

4769 

2158 

27.64 

40.29 

41941 

H 
15 

"     :    : 

As  forged 
Annealed 

.06993 
.06316 

747 
1985 

540 

24.50 

50-39 

15474 

16 

"     " 

1    ened 

.07066 

733 

- 

- 

- 

- 

17 

Silicon  steel 

As  forged 

.06163 

15148 

II073 

9-49 

1  2.6o 

45740 

18 

"        "          ... 

Annealed 

.06185 

14701 

8149 

7.80 

10.74 

36485 

'9 

"        "          ... 

I    ened 

•06195 

14696 

8084 

12.75 

17.14 

596i9 

20 

Chrome  steel     . 

As  forged 

.O2Ol6 

15778 

93^8 

12.24 

I3.87 

6i439 

21 

"         "... 

Annealed 

.01942 

14848 

7570 

8.98 

12.24 

42425 

22 

"         "... 

(    ened 

.02708 

13960 

8595 

38-15 

48.45 

1  6945  5 

23 

"         "... 

As  forged 

.01791 

14680 

7568 

18.40 

22.03 

85944 

24 

"         "... 

Annealed 

.01849 

13233 

6489 

15.40 

19.79 

64842 

25 

"... 

(  Oil-hard- 
{    ened 

•03035 

12868 

7891 

40.80 

56.70 

167050 

26 

Tungsten  steel  . 

As  forged 

.02249 

I57i8 

IOI44 

15.71 

17-75 

78568 

27 

" 

Annealed 

.02250 

16498 

II008 

I5-3° 

16.93 

80315 

C  Hardened 

28 

"            ".'•••. 

<    in  cold 

.02274 

- 

- 

- 

- 

- 

(    water 

(  Hardened 

29 

"            "... 

<    in  tepid 

.02249 

15610 

9482 

30.10 

34-70 

149500 

(    water 

30 

"     (French)   . 

(  Oil  hard- 
(    ened 

.03604 

14480 

8643 

47.07 

64.46 

216864 

31 

"            "... 

Very  hard 

.04427 

12133 

68l8 

51.20 

70.69 

197660 

32 

33 

Gray  cast  iron    . 
Mottled  cast  iron 

_ 

.11400 
.06286 

9148 
10546 

3l6l 

5108 

13-67 
12.24 

I7-03 

39789 
41072 

34 

White        " 

- 

.05661 

9342 

5554 

12.24 

20.40 

36383 

35 

Spiegeleisen 

.10520 

385 

77 

SMITHSONIAN  TABLES. 


277 


TABLE  287. 

PERMEABILITY   OF   SOME    OF   THE    SPECIMENS   IN    TABLE    286. 

This  table  gives  the  induction  and  the  permeability  for  different  values  of  the  magnetizing  force  of  some  of  the  speci- 
mens in  Table  286.  The  specimen  numbers  refer  to  the  same  table.  The  numbers  in  this  table  have  been  taken 
from  the  curves  given  by  Dr.  Hopkinson,  and  may  therefore  be  slightly  in  error ;  they  are  the  mean  values  for 
rising  and  falling  magnetizations. 


Magnetiz- 
ing force. 

Specimen  i  (iron). 

Specimen  8 
(annealed  steel). 

Specimen  g  (same  as 
8  tempered). 

Specimen  3 
(cast  iron). 

B 

M 

B 

/* 

B 

V- 

B 

M 

I 

_ 

_ 

_ 

_ 

_ 

_ 

265 

265 

2 

200 

100 

— 

— 

— 

— 

700 

35° 

3 

- 

- 

- 

- 

- 

- 

1625 

5 

IOO5O 

2OIO 

!525 

300 

750 

150 

3000 

600 

10 

12550 

1255 

9000 

900 

1650 

165 

5OOO 

500 

20 
30 

14550 
I52OO 

727 
5°7 

11500 
12650 

575 
422 

5»75 
9875 

294 
329 

6OOO 
6500 

300 
217 

40 

15800 

395 

13300 

332 

II600 

290 

7100 

177 

50 

16000 

320 

13800 

276 

I2OOO 

240 

735° 

149 

70 

100 

16360 
16800 

% 

J435° 
14900 

205 
149 

13400 
I45OO 

191 

145 

7900 
8500 

"3 

85 

150 

17400 

116 

15700 

105 

15800 

105 

9500 

63 

2OO 

17950 

90 

16100 

80 

l6lOO 

80 

10190 

51 

Tables  288-292  give  the  results  of  some  experiments  by  Du  Bois,*  on  the  magnetic  properties  of  iron,  nickel,  and 
cobalt  under  strong  magnetizing  forces.  The  experiments  were  made  on  ovoids  of  the  metals  18  centimetres  long 
and  0.6  centimetres  diameter.  The  specimens  were  as  follows:  (i)  Soft  Swedish  iron  carefully  annealed  and 
having  a  density  7.82.  (2)  Hard  English  cast  steel  yellow  tempered  at  230°  C. ;  density  7.78.  (3)  Hard  drawn 
best  nickel  containing  99  %  Ni  with  some  SiO2  and  traces  of  Fe  and  Cu ;  density  8.82.  (4)  Cast  cobalt  giving 
the  following  composition  on  analysis:  €0  =  93.1,  Ni  =  5-8,  Fe=:o.8,  Cu  =  o.2,  Si  =  o.i,  and  0  =  0.3.  The  speci- 
men was  very  brittle  and  broke  in  the  lathe,  and  hence  contained  a  surfaced  joint  held  together  by  clamps  during 
the  experiment.  Referring  to  the  columns,  ff,  B,  and  /u.  have  the  same  meaning  as  in  the  other  tables,  S  is  the 
magnetic  moment  per  gramme,  and  /  the  magnetic  moment  per  cubic  centimetre,  ff  and  S  are  taken  from  the 
curves  published  by  Du  Bois ;  the  others  have  been  calculated  using  the  densities  given. 

TABLE  288. 

MAGNETIC    PROPERTIES    OF    SOFT    IRON    AT    0°    AND    100°    C. 


Soft  iron  at  o°  C. 

Soft  iron  at  100°  C. 

H 

s 

/ 

B 

fi 

H 

* 

/ 

B 

ft 

IOO 

1  80.0 

1408 

17790 

177.9 

IOO 

ISO.O 

1402 

17720 

177.2  . 

2OO 

194.5 

1521 

19310 

96.5 

200 

194.0 

1511 

19190 

96.0 

400 
700 

208.0 

213.5 

1627 
1685 

20830 
21870 

52.1 
31.2 

4OO 
700 

2O7.O 
213.4 

1613 
1663 

20660 
21590 

51.6 
29.8 

IOOO 

218.0 

1705 

22420 

22.4 

IOOO 

215.0 

1674 

22040 

21.0 

I2OO 

218.5 

1709 

22670 

18.9 

I2OO 

215-5 

1679 

22300 

18.6 

TABLES  289. 

MAGNETIC    PROPERTIES    OF    STEEL    AT    O°    AND    1 00°    C. 


Steel  at  o°  C. 

Steel  at  100°  C. 

H 

s 

I 

B 

P 

H 

s 

I 

B 

J 

IOO 
2OO 
400 

165.0 
181.0 
193.0 

1283 
1408 
I5OO 

16240 
17900 
19250 

162.4 

89-5 
48.1 

IOO 
2OO 
400 

165.0 
180.0 

191.0 

1278 

T395 
1480 

16170 

17730 
19000 

161.7 

88.6 
47-5 

j   700 

199-5 

J552 

20210 

28.9 

700 

197.0 

1527 

19890 

28.4 

IOOO 

203-5 

1583 

2O9OO 

2O.9 

IOOO 

199.0 

J543 

20380 

20.4 

1200 

205.0 

1595 

2I24O 

17-7 

1500 

203.0 

1573 

21270 

14.2 

375ot 

212.0 

1650 

24470 

6.5 

3000 

205.5 

1593 

23020 

7-7 

5000 

208.0 

1612 

25260 

5.- 

*  "  Phil.  Mag."  5  series,  vol.  xxix. 

t  The  results  in  this  and  the  other  tables  for  forces  above  1200  were  not  obtained  from  the  ovoids  above  referred 
to,  but  from  a  small  piece  of  the  metal  provided  with  a  polished  mirror  surface  and  placed,  with  its  polished  face  nor- 
mal to  the  lines  of  force,  between  the  poles  of  a  powerful  electromagnet.  The  induction  was  then  inferred  from 
the  rotation  of  the  plane  of  a  polarized  ray  of  red  light  reflected  normally  from  the  surface.  (See  Kerr's  "  Constants," 
p.  292.) 


278 


TABLES  29O-296. 
MAGNETIC    PROPERTIES    OF    METALS. 

TABLE  290.  -  Cobalt  at  100°  C.  TABLE  291.  —Nickel  at  100°  0. 


H 

; 

7 

B 

» 

200 

1  06 

848 

10850 

54-2 

300 

116 

928 

11960 

39-9 

500 
700 

127 

1016 
1048 

13260 
13870 

26.5 
19.8 

IOOO 

134 

1076 

14520 

14-5 

1500 

'38 

1104 

15380 

10.3 

2500 

I43 

1144 

16870 

6.7 

4000 

'45 

1164 

18630 

4-7 

6000 

1176 

20780 

3-5 

9000 

149 

1192 

23980 

2.6 

At  o°  C.  this  specimen  gave  the  fol- 

lowing results  : 

7900 

154  |  1232 

23380 

3-0 

H 

S 

7 

B 

ft 

100 

35-o 

309 

3980 

39-8 

2OO 

43-° 

380 

4966 

24.8 

300 

46.0 

406 

5399 

1  8.0 

500 

50.0 

441 

6043 

I2.I 

700 

Sl-S 

454 

6409 

9.1 

IOOO 

53-o 

468 

6875 

6.9 

1500 

56.0 

494 

7707 

5i 

2500 

5*4 

515 

8973 

3-6 

4000 

59-o 

520 

10540 

2.6 

6000 

59-2 

522 

12561 

2.1 

9000 

59-4 

524 

15585 

i-7 

I2OOO 

Ato°C 

59-6 
.  this  sj 

526 
jecimer 

i  gave  th 

e  fol- 

lowing  results  : 

12300 

67-5 

595  |  19782 

1.6 

TABLE  292.  —  Magnetite. 

The  following  results  are  given  by  Du  Bois  *  for  a  specimen  of  magnetite. 


H 

/ 

B 

ft 

500 
IOOO 
2OOO 
I2OOO 

325 

345 
35° 
35° 

8361 
9041 
10084 
20084 

I6.7 
9-0 

5-° 
i-7 

Professor  Ewing  has  investigated  the  effects  of  very  intense  fields  on  the  induction  in  iron  and  other  metals.t  The 
results  show  that  the  intensity  of  magnetization  does  not  increase  much  in  iron  after  the  field  has  reached  an  in- 
tensity of  1000  c.  g.  s.  units,  the  increase  of  induction  above  this  being  almost  the  same  as  if  the  iron  were  not 
there,  that  is  to  say,  dB/  dff  is  practically  unity.  For  hard  steels,  and  particularly  manganese  steels,  much  higher 
forces  are  required  to  produce  saturation.  Hadfield's  manganese  steel  seems  to  have  nearly  constant  susceptibility 
up  to  a  magnetizing  force  of  io,coo.  The  following  tables,  taken  from  Ewing's  papers,  illustrate  the  effects  of 
strong  fields  on  iron  and  steel.  The  results  for  nickel  and  cobalt  do  not  differ  greatly  from  those  given  above. 


TABLE  293.  —  Lowmoor 
Wrought  Iron. 


TABLE  294.  —  Victor's 
Tool  Steel. 


TABLE   295.  —  Hadfield's 
Manganese  Steel. 


H 

7 

B 

V- 

3080 
6450 

1680 
1740 

24130 
28300 

7.83 

4-39 

10450 

'73° 

32250 

3-09 

13600 

1720 

35200 

2-S9 

16390 

1630 

36810 

2.25 

tyl? 

1680 

39900 

2.13 

18980 

173° 

40730 

2.15 

H 

7 

B 

p 

62IO 

M3° 

25480 

4.10 

9970 
I2I2O 

1570 
1550 

29650 
31620 

2.97 
2.60 

14660 

1580 

3455° 

2.36 

15530 

1610 

35820 

2.31 

H 

7 

B 

, 

I930 

2380 

335° 
5920 
6620 
7890 
8390 
9810 

84 
III 

I87 
191 

2620 

343° 
4400 

73*0 
8970 
10290 
11690 
14790 

1.36 
1.44 

•31 

.24 

•35 
•3° 
•39 
•51 

TABLE  296. —Saturation  Values  for  Steels  of  Different  Kinds. 


— 

!  !  —  —  

H 

7 

B 

M 

I 

2 

3 

Bessemer  steel  containing  about  0.4  per  cent  carbon  .  .  . 
Siemens-Marten  steel  containing  about  0.5  per  cent  carbon 
Crucible  steel  for  making  chisels,  containing  about  0.6  per 

17600 
18000 

19470 

1770 
1660 

1480 

39880 
38860 

38010 

2.27 
2.16 

I-9S 

4 

Finer  quality  of  3  containing  about  0.8  per  cent  carbon  .  . 

18330 
19620 

1580 

I4-4-O 

38190 
77600 

2.08 

I.  Q2 

\ 

18700 

icgo 

18710 

2.O7 

' 

*  "  Phil.  Mag."  5  series,  vol.  xxix. 


t  "  Phil.  Trans.  Roy.  Soc."  1885  and  1889. 


2/9 


TABLE  297. 

MAGNETIC    PROPERTIES    OF    IRON    IN    VERY   WEAK    FIELDS. 

The  effect  of  very  small  magnetizing  forces  has  been  studied  by  C.  Baur  *  and  by  Lord  Rayleigh.t  The  following 
short  table  is  taken  from  Baur's  paper,  and  is  taken  by  him  to  indicate  that  the  susceptibility  is  finite  for  zero  values 
of  H  and  for  a  finite  range  increases  in  simple  proportion  to  H.  He  gives  the  formula  k—  15  -f-  too  H,  or  f  = 


15  H  -\- 100 


H2.     The  experiments  were  made  on  an  annealed  ring  of  round  bar  1.013  cms.  radius,  the  ring  havin 
^.432  cms.     Lord  Rayleigh's  results  for  an  iron  wire  not  annealed  give  £  =  6.4 +  5.1  H,  or  7  =  6.4 


a  radius  of  9.432  cms.      .u/oro.   rtayieigii  s  resuus  iui  an  irun  wuc  nui  auiieaieu  give  n — -0.^-7-5.1  n,  or  / 
4-5.1  //2.     The  forces  were  reduced  as  low  as  0.00004  c-  g-  s->  the  relation  of  k  to  //  remaining  constant. 


First  experiment. 

Second  experiment. 

H 

k 

7 

H 

k 

.OI  580 
.03081 
.07083 
.13188 
.23011 
.38422 

16.46 

I7-65 
23.00 
28.90 
39.81 
58.56 

2.63 

5-47 
i6-33 
3    ^  5 

91.56 
224.87 

.0130 
.0847 
.0946 
.1864 
.2903 

•3397 

20.49 
25.07 
32.40 
35-20 

TABLES  298,  299. 

DISSIPATION    OF    ENERGY    IN    CYCLIC    MAGNETIZATION    OF    MAGNETIC 

SUBSTANCES. 

When  a  piece  of  iron  or  other  magnetic  metal  is  made  to  pass  through  a  closed  cycle  of 
magnetization  dissipation  of  energy  results.  'Let  us  suppose  the  iron  to  pass  from  zero  magneti- 
zation to  strong  magnetization  in  one  direction  and  then  gradually  back  through  zero  to  strong 
magnetization  in  the  other  direction  and  thence  back  to  zero,  and  this  operation  to  be  repeated 
several  times.  The  iron  will  be  found  to  assume  the  same  magnetization  when  the  same  magne- 
tizing force  is  reached  from  the  same  direction  of  change,  but  not  when  it  is  reached  from  the 
other  direction.  This  has  been  long  known,  and  is  particularly  well  illustrated  in  the  permanency  of 
hard  steel  magnets.  That  this  fact  involves  a  dissipation  of  energy  which  can  be  calculated  from 
the  open  loop  formed  by  the  curves  giving  the  relation  of  magnetization  to  magnetizing  force  was 
pointed  out  by  Warburg  |  in  1881,  reference  being  made  to  experiments  of  Thomson,  §  where  such 
curves  are  illustrated  for  magnetism,  and  to  E.  Cohn,  ||  where  similar  curves  are  given  for  thermo- 
electricity. The  results  of  a  number  of  experiments  and  calculations  of  the  energy  dissipated 
are  given  by  Warburg.  The  subject  was  investigated  about  the  same  time  by  Ewing,  who  pub- 
lished results  somewhat  later.  ^[  Extensive  investigations  have  since  been  made  by  a  number  of 
investigators. 


TABLE  298.-  Soft  Iron  Wire. 

(From  Ewing's  1885  paper.) 


Horse- 

Total 
induction 

Dissipation 
of  energy 

power 
wasted  per 

per  sq.  cm. 

in  ergs  per 

ton  at  100 

B 

cu.  cm. 

cycles  per 

sec. 

2OOO 

420 

0.74 

3000 

800 

1.41 

4OOO 

1230 

2.18 

5000 

1700 

3-01 

6000 

22OO 

3.89 

7OOO 

2760 

4.88 

8000 

3450 

6.10 

9000 

42OO 

7-43 

IOOOO 

5OOO 

8.84 

IIOOO 

5820 

10.30 

12000 

6720 

11.89 

I3OOO 

7650 

J3-53 

I4OOO 
15000 

8650 
9670 

15-30 
17.10 

"Wied.  Ann."  vol.  xi. 

"  Wied.  Ann.''  vol.  xiii.  p.  141. 

"  Wied.  Ann."  vol.  6. 


SMITHSONIAN  TABLES. 


TABLE  299.  -  Gable  Transformers. 

This  table  gives  the  results  obtained  by  Alexander  Siemens  with  one  of 
Siemens'  cable  transformers.  The  transformer  core  consisted  of  900 
soft  iron  wires  i  mm.  diameter  and  6  metres  long.**  The  dissipation 
of  energy  in  watts  is  for  100  complete  cycles  per  second. 


Mean  maxi- 
mum induc- 
tion density 
in  core. 
B 

Total  ob- 
served dis- 
sipation of 
energy  in  the 
core  in  watts 
per  112  Ibs. 

Calculated 
eddy  current 
loss  in  watts 
per  ii2  Ibs. 

Hysteresis 
loss  of 
energy  in 
watts  per 
1  12  Ibs. 

Hysteresis 
loss  of 
energy  in 
ergs  per 
cu.  cm. 
per  cycle. 

IOOO 

43-2 

4 

39-2 

602 

2000 

96.2 

16 

8o.2 

1231 

3000 
4OOO 

158.0 
231.2 

* 

I22.O 
I67.2 

1874 
2566 

5000 

309-5 

IOO 

209.5 

3217 

6000 

39O.I 

144 

246.1 

3779 

t  "  Phil.  Mag."  vol.  xxiii. 

§  "  Phil.  Trans.  Roy.  Soc/'  vol.  175. 

"  Proc.  Roy.  Soc.''  1882,  and  "  Trans.  Roy.  Soc."  1885. 


"  Proc.  Inst.  of  Elect.  Eng."  Lond.,  1892. 
280 


TABLE  30O. 

DISSIPATION  OF  ENERGY  IN  THE  CYCLIC  MAGNETIZATION  OF  VARIOUS 

SUBSTANCES. 

C.  P.  Steinmetz  concludes  from  his  experiments*  that  the  dissipation  of  energy  due  to 
hysteresis  in  magnetic  metals  can  be  expressed  by  the  formula  e  =  aBl-&,  where  e  is  the  energy 
dissipated  and  a  a  constant.  He  also  concludes  that  the  dissipation  is  the  same  for  the  same 
range  of  induction,  no  matter  what  the  absolute  value  of  the  terminal  inductions  may  be.  His 
experiments  show  this  to  be  nearly  true  when  the  induction  does  not  exceed  -j-  15000  c.  g.  s. 
units  per  sq.  cm.  It  is  possible  that,  if  metallic  induction  only  be  taken,  this  may  be  true  up  to 
saturation  ;  but  it  is  not  likely  to  be  found  to  hold  for  total  inductions  much  above  the  satura- 
tion value  of  the  metal.  The  law  of  variation  of  dissipation  with  induction  range  in  the  cycle, 
stated  in  the  above  formula,  is  also  subject  to  verification.t 

Values  of  Constant  «. 


The  following  table  gives  the  values  of  the  constant  a  as  found  by  Steinmetz  for  a  number  of  different  specimens. 
The  data  are  taken  from  his  second  paper. 


Number  of 
specimen. 

Kind  of  material. 

Description  of  specimen. 

Value  of 
a. 

I 

Iron  . 

Norway  iron      

.00227 

2 

" 

Wrought  bar     

.00326 

3 

"      . 

Commercial  ferrotype  plate      ..... 

.00548 

4 

M 

Annealed             "             "          

.00458 

5 

" 

Thin  tin  plate    

.00286 

6 

" 

Medium  thickness  tin  plate       

.00425 

*7 

Steel  . 

•OO74.Q 

8 

Annealed  cast  steel  

ww,3  HV 

.00848 

9 

" 

Soft  annealed  cast  steel    

.00457 

10 

" 

Very  soft  annealed  cast  steel    

.00318 

ii 

" 

Same  as  8  tempered  in  cold  water    .... 

.02792 

12 

« 

Tool  steel  glass  hard  tempered  in  water 

.07476 

'3 

" 

"        "      tempered  in  oil          

.02670 

I  A 

it 

01800 

1  T- 

15 
16 

"                     } 

(  Same  as  12,  13,  and  14,  after  having  been  subjected  ) 
1  to   an  alternating  m.  m.  f.  of  from  4000  to  6000  > 

(  .06130 
]  .02700 

i? 

"                  •  ) 

(  ampere  turns  for  demagnetization    .         .         .         .  ; 

(  .01445 

18 

Cast  iron  . 

Gray  cast  iron  ........ 

.01300 

19 

"         "     . 

"        "       "     containing  $  %  aluminium 

•01365 

20 

«         « 

"        "       "                        |%                             .         . 

.01459 

21 

Magnetite  . 

f  A  square  rod  6  sq.  cms.  section  and  6.5  cms.  long,  ) 
J  from   the  Tilly  Foster  mines,  Brewsters,    Putnam  > 

.02348 

(  County,  New  York,  stated  to  be  a  very  pure  sample  ) 

22 

Nickel 

Soft  wire  

.0122 

(  Annealed    wire,     calculated    by    Steinmetz    from  ) 

_/; 

23 

j  Ewing's  experiments         ) 

.0156 

24 

M 

Hardened,  also  from  Ewing's  experiments 

•0385 

25 

Cobalt       . 

(  Rod  containing  about  2  %  of  iron,  also  calculated  ) 
|  from  Ewing's  experiments  by  Steinmetz           .         .  J 

.OI2O 

Consisted   of   thin   needle-like   chips  obtained   by 

milling  grooves  about  8  mm.  wide  across  a  pile  of 

thin  sheets  clamped  together.     About  30  %  by  vol- 

26 

Iron  filings 

ume  of  the  specimen  was  iron, 
ist  experiment,  continuous  cyclic  variation  of  m.  m.  ) 
f.  180  cycles  per  second     ) 

•0457 

2c\  experiment,  114  cycles  per  second 

.0396 

[  3d           "             79~9X  cycles  per  second  . 

•0373 

*  "Trans.  Am.  Inst.  Elect.  Eng.''  January  and  September,  1892. 
t  See  T.  Gray,  "  Proc.  Roy.  Soc."  vol.  Ivi. 


SMITHSONIAN  TABLES. 


281 


TABLE    3O1 . 

DISSIPATION   OF   ENERGY  IN   THE   CYCLIC    MAGNETIZATION   OF  TRANS- 
FORMER CORES.* 

This  table  gives,  for  the  most  part,  results  obtained  for  transformer  cores.  The  electromagnet  core  formed  a  closed 
iron  circuit  of  about  320  sq.  cms.  section  and  was  made  up  of  sheets  of  Bessemer  steel  about  1-20  inch  thick.  The 
No.  20  transformer  had  a  core  of  soft  steel  sheets  about  7-1000  inch  thick  insulated  from  each  other  by  sheets  of 
thin  paper.  The  cores  of  the  other  transformers  were  formed  of  soft  steel  sheets  15-1000  inch  thick  insulated  from 
each  other  by  their  oxidized  surfaces  only.  The  following  are  the  particulars  of  the  data  given  in  the  different 
columns :  — 

Column  i.  Description  of  specimen. 

"      2.  The  total  energy,  in  joules  per  cycle,  required  to  produce  the  magnetic  induction  given  in  column  B 

"       3.  The  energy,  in  joules  per  cycle,  returned  to  the  circuit  on  reversal  of  the  magnetizing  force. 

"       4.  The  energy  dissipated,  in  joules  per  cycle,  or  the  difference  of  columns  2  and  3. 

"       5,  6,  and  7.  The  quantities  in  columns  2,  3,  and  4  reduced  to  ergs  per  cubic  centimetre  of  the  core. 

"      B,  The  maximum  induction  in  c.  g.  s.  units  per  sq.  cm. 


1 

2 

3 

4 

5 

6 

7 

B 

6-5 

0.9 

5.6 

1010 

140 

867 

2660 

m 

2.6 

10.4 

21.8 

56.4 

3800 
10400 

406 
1620 

3400 
8800 

6700 
Il6oo 

8i.4 

15-4 

66.0 

12700 

2400 

10300 

12700 

Electromagnet.  .  .  .  - 

96.6 
126.2 

21.8 

38.2 

74-8 
88.0 

15100 

19700 

3400 
3960 

11700 
13700 

I4IOO 
15200 

153.0 

57.6 

95-4 

23900 

8990 

14900 

'5900 

178.4 

79.2 

99.2 

27800 

12400 

15500 

16600 

221.2 

116.8 

1044 

34500 

18300 

16300 

17240 

275.6 

168.0 

107.6 

42900 

26200 

16800 

17420 

I.3I 

0.30 

I.OI 

1435 

328 

1107 

2330 

4-65 

I.IO 

3-55 

5110 

I2IO 

3900 

4980 

Westinghouse  No  20 

8.25 

1.62 

6.63 

9060 

1780 

7280 

6620 

transformer  .  .  .  . 

10.36 

1.89 

8.47 

11  35° 

2O7O 

9280 

7720 

I2.2O 

2.98 

9.22 

13440 

3280 

10160 

8250 

18.20 

5-*5 

13-05 

19980 

5660 

14320 

9690 

0-45 

0.055 

0.400 

875 

IO5 

770 

3480 

Westinghouse  No.  8 
transformer,  specimen  I 

0.80 

1.66 

2.42 

0.102 
0.199 
0.406 

O.IOI 

1.460 

2.OIO 

1544 
3200 
4650 

780 

1348 
2820 
3870 

7570 
9250 

I 

3-54 

0-795 

2-75° 

6820 

r53° 

5290 

10940 

f 

0-399 

0.046 

0-353 

768 

88 

680 

3060 

Westinghouse  No.  8 

0.820 

0.085 

0-735 

1574 

164 

1410 

4830 

transformer,  specimen  2  1 

1.713 

0.183 

3300 

352 

2948 

7570 

I 

2.663 

0-343 

2.320 

5120 

660 

4460 

9270 

f 

0.488 

0.062 

0.426 

1360 

172 

1188 

4640 

Westinghouse  No.  6 

0.814 

0.096 

0.718 

2260 

266 

1994 

6760 

transformer,  specimen  1  1 

1.430 

0.205 

1.225 

3980 

570 

9370 

1 

2.000 

0.33° 

1.670 

5560 

918 

4642 

10950 

f 

0.722 

O.IOO 

0.622 

2OOO 

278 

1722 

7290 

Westinghouse  No.  6 

1.048 

0.164 

0.884 

2920 

456 

2464 

9000 

transformer,  specimen  2  1 

1-379 

0.222 

1.157 

3830 

616 

32I4 

9990 

I 

I-731 

0.328 

1.403 

4810 

912 

3898 

II2IO 

Westinghouse  No.  4 
transformer  ....  1 

0-355 
Q-549 
0-783 

0.044 
0.074 
O.I26 

0.3II 

0-475 
0.657 

I2IO 
1880 
2690 

255 
433 

1058 
1625 

2257 

4540 
CQ20 

7  '40 

I 

0.970 

0.175 

o-795 

3340 

603 

2737 

7800 

Thomson-Houston  1500  1 

0.413 
0.681 

0.105 
0.189 

0.308 
0.492 

1930 
3190 

490 
880 

1440 
2310 

6150 
8250 

watt  transformer   .  .  1 

1.207 

0.389 

0.818 

1830 

3830 

IIIIO 

I 

1-797 

0.710 

1.087 

§420 

3320 

5100 

13290 

*  T.  Gray,  from  special  experiments ;  see  Table  285  for  other  properties. 
SMITHSONIAN  TABLES. 

282 


TABLE  3O2, 


DISSIPATION   OF   ENERGY   DUE   TO   MAGNETIC   HYSTERESIS   IN   IRON.* 

The  first  column  gives  the  maximum  magnetic  induction  B  per  square  centimetre  in  c.  g.  s.  units.     The  other  col- 
umns give  the  dissipation  of  energy  in  ergs  per  cycle  per  cubic  centimetre  for  the  iron  specified  in  the  foot-note. 


B 

1 

2 

3 

4 

5 

6 

7 

2000 

400 

420 

530 

000 

750 

93° 

IIOO 

3OOO 

780 

800 

1050 

1150 

1350 

1700 

2150 

4000 

1200 

1260 

1670 

1780 

2030 

2600 

3300 

5OOO 

1680 

1770 

2440 

2640 

2810 

3800 

4700 

6000 

2200 

2370 

3170 

336° 

3700 

5200 

6200 

7000 

2800 

3150 

4020 

4300 

4650 

6600 

7800 

8000 

3430 

3940 

5020 

5300 

5770 

8400 

9500 

9000 

4160 

4800 

6100 

6380 

6970 

IOIOO 

11400 

10000 

4920 

5730 

7200 

7520 

8340 

11800 

13400 

IIOOO 

5800 

6800 

8410 

8750 

9880 

13600 

15600 

12000 

6700 

8000 

975° 

10070 

"55° 

15400 

- 

13000 

7620 

9200 

II200 

11460 

13260 

17300 

- 

I4OOO 

8620 

10500 

12780 

13100 

15180 

- 

- 

I5OOO 

9730 

12150 

14600 

14900 

17300 

- 

- 

The  iron  for  which  data  are  given  in  columns  i  to  7  is  described  as  follows  :  — 

i.  Very  soft  iron  wire  (taken  from  a  former  paper). 

2a.  Sheet  iron  1.95  millimetres  thick            )  almost  alike. 

2b.  Thin  sheet  iron  0.367  millimetres  thick  ) 

3.  Iron  wire  0.975  millimetres  diameter. 

4.  Iron  wire  of  hedgehog  transformer  0.602  millimetres  diameter. 

5.  Thin  sheet  iron  0.47  millimetres  thick. 

6.  Fine  iron  wire  0.2475  millimetres  diameter. 

7.  Fine  iron  wire  0.34  millimetres  diameter. 

*  Ewing  and  Klassen,  "  Phil.  Trans.  Roy.  Soc."  vol.  clxxxiv.  A,  p.  1015. 


283 


TABLE  3O3. 

MAGNETO-OPTIC  ROTATION. 

Faraday  discovered  that,  when  a  piece  of  heavy  glass  is  placed  in  magnetic  field  and  a  beam 
of  plane  polarized  light  passed  through  it  in  a  direction  parallel  to  the  lines  of  magnetic  force, 
the  plane  of  polarization  of  the  beam  is  rotated.  This  was  subsequently  found  to  be  the  case 
with  a  large  number  of  substances,  but  the  amount  of  the  rotation  was  found  to  depend  on  the 
kind  of  matter  and  its  physical  condition,  and  on  the  strength  of  the  magnetic  field  and  the 
wave-length  of  the  polarized  light.  Verdet's  experiments  agree  fairly  well  with  the  formula  — 


where  c  is  a  constant  depending  on  the  substance  used,  /  the  length  of  the  path  through  the 
substance,  H  the  intensity  of  the  component  of  the  magnetic  field  in  the  direction  of  the  path 
of  the  beam,  r  the  index  of  refraction,  and  A.  the  wave-length  of  the  light  in  air.  If  H  be  dif- 
ferent, at  different  parts  of  the  path,  IH  is  to  be  taken  as  the  integral  of  the  variation  of  mag- 
netic potential  between  the  two  ends  of  the  medium.  Calling  this  difference  of  potential  v,  we 
may  write  6=  Av,  where  A  is  constant  for  the  same  substance,  kept  under  the  same  physical 
conditions,  when  the  one  kind  of  light  is  used.  The  constant  A  has  been  called  "  Verdet's  con- 
stant," *  and  a  number  of  values  of  it  are  given  in  Tables  303-310.  For  variation  with  tempera- 
ture the  following  formula  is  given  by  Bichat :  — 

X  =  J?0  (I— 0.00104 /— 0.00001 4/2), 

which  has  been  used  to  reduce  some  of  the  results  given  in  the  table  to  the  temperature  corre- 
sponding to  a  given  measured  density.  For  change  of  wave-length  the  following  approximate 
formula,  given  by  Verdet  and  Becquerel,  may  be  used  :  — 


where  JJL  is  index  of  refraction  and  A  wave-length  of  light. 

A  large  number  of  measurements  of  what  has  been  called  molecular  rotation  have  been  made, 
particularly  for  organic  substances.  These  numbers  are  not  given  in  the  table,  but  numbers 
proportional  to  molecular  rotation  may  be  derived  from  Verdet's  constant  by  multiplying  in  the 
ratio  of  the  molecular  weight  to  the  density.  The  densities  and  chemical  formulae  are  given  in 
the  table.  In  the  case  of  solutions,  it  has  been  usual  to  assume  that  the  total  rotation  is  simply 
the  algebraic  sum  of  the  rotations  which  would  be  given  by  the  solvent  and  dissolved  substance, 
or  substances,  separately;  and  hence  that  determinations  of  the  rotary  power  of  the  solvent 
medium  and  of  the  solution  enable  the  rotary  power  of  the  dissolved  substance  to  be  calculated. 
Experiments  by  Quincke  and  others  do  not  support  this  view,  as  very  different  results  are 
obtained  from  different  degrees  of  saturation  and  from  different  solvent  media.  No  results  thus 
calculated  have  been  given  in  the  table,  but  the  qualitative  result,  as  to  the  sign  of  the  rotation 
produced  by  a  salt,  may  be  inferred  from  the  table.  For  example,  if  a  solution  of  a  salt  in  water 
gives  Verdet's  constant  less  than  0.0130  ate2o°  C.,  Verdet's  constant  for  the  salt  is  negative. 

The  table  has  been  for  the  most  part  compiled  from  the  experiments  of  Verdet,t  H.  Becque- 
rel,J  Quincke,  §  Koepsel,||  Arons,1[  Kundt,**  Jahn,tt  Schonrock,JJ  Gordon,  §§  Rayleigh  and 
Sidgewick,||||  Perkin,lf  Bichat.*** 

As  a  basis  for  calculation,  Verdet's  constant  for  carbon  disulphide  and  the  sodium  line  D  has 
been  taken  as  0.0420  and  for  water  as  0.0130  at  20°  C. 

*  The  constancy  of  this  quantity  has  been  verified  through  a  wide  range  of  variation  of  magnetic  field  by  H.  E, 
J.  G.  Du  Bois  (Wied.  Ann.  vol.  35). 

t  "  Ann.  de  Chim.  et  de  Phys."  [3]  vol.  52. 

%  "  Ann.  de  Chim.  et  de  Phys."  [5]  vol.  12  ;  "  C.  R."  vols.  90  and  100. 
§    'Wied.  Ann."  vol.  24. 
Wied.  Ann."  vol.  26. 
Wied.  Ann."  vol.  24. 
Wied.  Ann."  vols.  23  and  27. 
tt    '  Wied.  Ann."  vol.  43- 
l\    '  Zeits.  fur  Phys.  Chem."  vol.  n. 
Proc.  Roy.  Soc."  1883. 
Phil.  Trans.  R.  S."  1885. 
Jour.  Chem.  Soc."  vols.  8  and  12. 
Jour,  de  Phys."  vols.  8  and  9. 

SMITHSONIAN  TABLES. 

284 


TABLE  303. 


MAGNETO-OPTIC  ROTATION. 

Solids. 


Substance. 

Chemical 
formula. 

Density 
or 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

Temp.  C. 

Authority. 

Amber       . 

- 

- 

D 

0.0095 

18-20° 

Quincke. 

Blende      

ZnS 

_ 

« 

O.221.4 

1C 

Becquerel. 

Diamond  

C 

- 

H 

3  * 

0.0127 

J 

« 

Fluor  spar        .... 

CaFl2 

- 

(( 

0.0087 

« 

« 

Glass  : 

« 

0.0203 

(« 

tt 

Faraday  A    .... 

- 

5458 

«{ 

0.0782 

1  8-20 

Quincke. 

B    .        . 

- 

4.284 

« 

0.0649 

« 

« 

Flint      .        .        . 

_ 

_ 

« 

0.0420 

« 

<« 

M 

0.0^2  c 

1C 

Becquerel. 



- 

- 

U 

^  ^3     J 
0.0416 

J 

« 

"      dense  .... 

- 

- 

« 

O.O576 

(( 

« 

"       .        .        .        . 

- 

- 

« 

0.0647 

U 

« 

Plate      

- 

- 

« 

O.O4O6 

1  8-20 

Quincke. 

Lead  borate      .... 

PbB2O4 

- 

« 

0.0600 

15 

Becquerel. 

Quartz  (perpendicular  to  axis) 

- 

-    ' 

« 

O.OI72 

1  8-20 

Quincke. 

Rock  salt          .... 

NaCl 

- 

a 

0.0355 

15 

Becquerel. 

Selenium  ..... 

Se 

- 

B 

0.4625 

n 

(C 

Sodium  borate 

Na2B4O7 

- 

D 

0.0170 

« 

«« 

Spinel  (colored  by  chrome) 

- 

- 

« 

O.O2O9 

« 

« 

Sylvine      

KC1 

- 

« 

0.0283 

« 

(« 

Ziqueline  (suboxide  of  copper) 

Cu2O 

- 

B 

0.5908 

«( 

(« 

SMITHSONIAN  TABLES. 


285 


TABLE  304. 


MAGNETO-OPTIC    ROTATION, 

Liquids. 


Substance. 

Chemical 
formula. 

Density 
in 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

Temp. 
C. 

Authority. 

C3H6O 

0.7947 

D 

o.oi  13 

2O 

Jahn. 

O.vqc;? 

o.oi  15 

J  C 

Per  kin 

• 
Acids  :    (see  also  solutions  in 
water) 

u 

C2H4O2 

0.7947 
1.0561 

H 

« 

O.OII4 

o  0105 

!i 

21 

Schonrock. 
Perkin 

Butyric  
Formic  
Hydrochloric 

Hydrobromic 
Hydroiodic  .... 
Nitric    .        .        .        .        . 
"      (fuming)      . 
Propionic      .... 
Sulphuric      .... 
Sulphurous   .... 
Valeric          .... 

C4H802 
CH202 
HC1 

HBr 
HI 
HN03 

C3H602 
H2S04 
H2S03 

0.9663 
.2273 
.2072 

•7859 
•9473 
.5190 

09975 

O.94"?S 

« 

U 

it 

u 

o.oi  16 
0.0105 
0.0224 
0.0206 

0.0343 
0.0513 

0.0070 
0.0080 

O.OI1O 
O.OI  21 
0.0153 
O.OI  2  1 

15 
IS 
15 
15 

15 

J5 
13 
«S 

15 
15 
'5 

1  c 

Becquerel.    ! 
Perkin. 

u 

Becquerel. 
Perkin. 
Becquerel. 

Perkin. 

Alcohols  : 

CsHnOH 

l< 

O.OI3I 

I  c 

Becquerel. 

O.8lO7 

(1 

O.OI28 

20 

Jahn. 

C4H9OH 

0.802  1 

II 

O  OI24 

20 

tt 

u 

o  or  "•  A. 

I  c 

Ethyl     

C2H5OH 

O.7O2O 

u 

0.0107 

1  8-20 

Ouincke 

O.7QOO 

M 

O.O  I  I  ^ 

2O 

Jahn 

M 

M 

0.7944 

u 

o.oi  14 

I  c 

Perkin. 

« 

« 

O-7Q47 

M 

o.oi  13 

16 

Schbnrock 

Methyl           .... 

CH3OH 

O.7QI  S 

M 

O  OOQ4. 

1  8—^0 

Ouincke 

M 

07920 

« 

0.0093 

o.o  i  o'o 

20 
I  c 

Jahn. 
Becquerel 

u 

« 

0.7066 

M 

0.0096 

I  c 

Perkin 

« 
Octyl     

« 

C8Hi7OH 

0.7903 

0.8206 

0.0096 

O.O  I  74 

21.9 

15 

Schonrock. 
Perkin 

Propyl  
« 

C3H7OH 

H 

0.8050 
0.8082 

M 

0.0120 
O.O  I  2O 
0.0118 

20.8 
I5.0 
I  c 

Schonrock. 
Perkin. 
Becquerel 

M 

Benzene    

M 

C6H6 
« 

0.8042 
0.8786 

u 
« 

O.OI  2O 

0.0297 

20 
2O 
15 

Jahn. 
Jahn. 
Becquerel 

« 

Bromides  : 
Bromoform  .... 
Ethyl     

Ethylene        .... 
« 

Methyl.        !.'.'! 
Methylene     .... 
Octyl     
Propyl  
Carbon  d  'sulphide    . 
«               « 

«               « 
«               « 
«               «« 
«               <« 

«< 

CHBr3 
C2H5Br 
C2H4Br2 

CH3Br 
CH2Br2 
C8H17Br 
C3H7Br 
CS2 

it 

H 

« 
« 

0.8718 
2.9021 

1.4486 
2.1871 
2.1780 

1-7331 
2.4971 
1.1170 
1.3600 

1.2644 

(« 

«( 

M 
« 
H 

n 

i< 

« 

« 
«« 

« 

0.0301 

0.0317 

0.0183 
0.0268 
0.0269 
0.0205 
0.0276 
0.0164 
0.0180 
0.0441 

0.0434 
0.0433 

0.0420 
0.0420 

0.0439 

26.9 

15 
15 
15 
20 
O 

«s 

15 

1  8-20 

o 

o 
18 
18 

0 

Schonrock. 
Perkin. 

u 

Jahn. 
Perkin. 

Quincke. 
(  Becquerel, 
\      1885. 
Gordon. 
Rayleigh. 
Koepsel. 
Arons. 

SMITHSONIAN  TABLES. 


286 


TABLE   304, 


MAGNETO-OPTIC  ROTATION 

Liquids. 


Substance. 

Chemical 
formula. 

Density 
in 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

Temp. 

Authority. 

Chlorides: 

Amyl   

CHC1 

0.8740 

D 

0.0140 

2O 

Jahn. 

Arsenic         .... 

As 

- 

u 

0.0422 

15 

Becquerel. 

Carbon         .... 

C 

— 

" 

0.0170 

15 

" 

bichloride 

CC14 

_ 

" 

0.0321 

15 

" 

Chloroform 

CHC13 

1.4823 

u 

0.0164 

20 

Jahn. 

"          .... 

" 

1.4990 

" 

0.0166 

15 

Perkin. 

Ethyl   

C2H5C1 

0.0,160 

(1 

0.0138 

fa 

« 

Ethylene      .... 

C2H4C12 

~'y~*fy 

« 

0.0166 

15 

« 

"             .... 

11 

1.2561 

" 

0.0164 

20 

Jahn. 

Methyl         .... 
Methylene  .... 

CH3C1 
CH2C12 

L336I 

H 

0.0170 
0.0162 

15 
15 

Becquerel. 
Perkin. 

Octyl    

C8H17C1 

0.8778 

" 

0.0141 

15 

« 

Phosphorus  protochloride  . 
Propyl          .... 

PC13 
C3H7C1 

0.8922 

I 

0.0275 
0.0135 

15 
IS 

Becquerel. 
Perkin. 

Silicon          .... 
Sulphur  bichloride 

SiCl4 
S2C12 

_ 

I 

0.0275 
0.0393 

15 
15 

Becquerel. 

Tin  bichloride 

SnCl4 

— 

" 

0.0151 

IS 

M 

Zinc  bichloride    . 

ZnCli 

- 

" 

0.0437 

15 

" 

Iodides  : 

Ethyl    

C2H5I 

I.94I7 

« 

0.0296 

15 

Perkin. 

Methyl          .... 

CH3I 

2.2832 

H 

0.0336 

15 

u 

Octyl    ..... 

C8H17I 

T-3395 

" 

0.0213 

15 

" 

Propyl  ..... 

C8H7I 

1.7658 

" 

0.0271 

" 

Nitrates  : 

Ethyl   

C2H5O.NO2 

1.1149 

« 

0.0091 

15 

« 

Ethylene  (nitroglycol) 

C2H4(NO3)2 

1.4948 

' 

0.0088 

15 

" 

Methyl          .... 

CH3O.NO2 

1.2157 

< 

0.0078 

15 

" 

Propyl          .... 

C3H7O.N02 

1.0622 

• 

O.OIOO 

15 

" 

Trinitrin  (nitroglycerine)     . 

C3H5(N03)3 

1.5996 

1 

0.0090 

15 

" 

Nitro  ethane 

C2H5N02 

1.0552 

' 

0.0095 

15 

" 

Nitro  methane     . 

CH3NO2 

1.1432 

• 

0.0084 

15 

M 

Nitro  propane 

C3H5NO2 

I.OIOO 

' 

O.OIO2 

15 

M 

Paraffins  : 

Decane         .... 

CioH22 

0.7218 

" 

0.0128 

23.1 

Schonrock. 

Heptane       .... 

0.6880 

" 

O.OI25 

15 

Perkin. 

Hexane        .... 

CeHi4 

0.6580 

" 

O.OI22 

22.1 

Schonrock. 

"              .... 

" 

0.6743 

It 

0.0125 

15 

Perkin. 

Octane         .... 

CgHig 

0.7011 

u 

O.OI28 

23.1 

Schonrock. 

Pentane        .... 

CsHi2 

0.6196 

" 

O.OII9 

21.  1 

" 

"              .... 

u 

0.6332 

" 

O.OIlS 

15 

Perkin. 

Phosphorus  (melted) 
Sulphur  (melted)     . 

p 

S 

M 
H 

0.1316 
0.0803 

33 
114 

Becquerel. 
M 

Toluene           .... 

C7H8 

0.8581 

u 

0.0269 

28.4 

Schonrock. 

"                 .... 

" 

- 

" 

0.0243 

15 

Becquerel. 

Water    

H2O 

0.9992 

*< 

0.0130 

I  c 

*< 

H 

o.oi  31 

1  J 

18-20 

Quincke. 

« 

M 

0.9983 

« 

0.0132 

20 

Jahn. 

Xylene  '. 

C8H10 

« 

O.O22I 

15 

Becquerel. 

.        .        . 

0.8746 

0.0263 

27 

Schonrock. 

SMITHSONIAN  TABLES. 


287 


TABLE  305. 


MAGNETO-OPTIC   ROTATION, 

Solutions  of  Acids  and  Salts  in  Water. 


Substance. 

Chemical 
formula. 

Density, 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in  minutes 

Temp. 

Authority. 

C3H6O 

O.Q7I5 

D 

O.OI29 

20° 

Jahn. 

Acids  : 

y/     D 

Hydrobromic 

HBr 

I-7859 

« 

0-0343 

15 

Perkin. 

"                   ... 

M 

I.6I04 

M 

0.0304 

" 

<« 

"                   ... 

" 

1-3775 

" 

0.0244 

« 

« 

"                                   •           ''    .                . 

** 

1.2039 

U 

0.0194 

<« 

H 

« 

U 

1.1163 

U 

0.0168 

" 

(« 

Hydrochloric        . 

HC1 

1.2072 

« 

O.O225 

* 

" 

"                  .        •        • 

" 

1.1856 

«« 

O.O2I9 

" 

<« 

« 

" 

I-I573 

H 

O.O2O4 

M 

«( 

u 

« 

« 
« 

1.1279 
1.0762 

«« 

« 

0.0193 
0.0168 

« 

«« 
N 

M 

M 
U 

1.0323 
1.0158 

«< 

0.0150 
O.OI4O 

20 

Jahn. 

Hydriodic     .... 

HI 

1-9473 

" 

0-0513 

" 

Perkin. 

« 

M 

1-9057 

H 

0.0499 

M 

«« 

"             .... 

11 

1.8229 

M 

0.0468 

« 

« 

M 

(t 

1.7007 

" 

0.0421 

«( 

" 

M 

" 

1-4495 

<« 

0.0323 

" 

" 

(( 

" 

1.2966 

(« 

0.0258 

H 

<« 

« 

« 

1.1760 

«( 

0.0205 

" 

" 

Nitric    

HNO3 

1.5190 

«« 

O.OOIO 

« 

H 

"        

" 

I-3560 

(« 

0.0105 

« 

'< 

Sulphuric  -|-  3H2O      . 
Ammonia         .        .        .        . 

H2SO4 
NH3 

0.8918 

H 

«« 

O.OI2I 
0.0153 

15 

Becquerel. 
Perkin. 

Bromides  : 

Ammonium  .... 

NH4Br 

1.2805 

<« 

O.O226 

« 

M 

u 

" 

1.1576 

" 

0.0186 

M 

« 

Barium         .... 
u 

BaBr2 

1-5399 

i  28^1; 

M 

0.0215 
0.0176 

2O 
M 

Jahn. 

«< 

Cadmium     .... 

CdBr2 

L.4.U  ^JJ 
I.329I 

« 

0.0192 

U 

M 

« 

« 

1.1608 

" 

0.0162 

" 

" 

Calcium        .        .        .        . 

CaBr2 

1.2491 

M 

0.0189 

U 

« 

"           -  .        . 

" 

I-I337 

M 

0.0164 

M 

M 

Potassium     . 

KBr 

1.1424 

« 

0.0163 

« 

«« 

"          ..... 

« 

1.0876 

M 

0.0151 

M 

« 

Sodium         .... 

NaBr 

i-i35i 

( 

0.0165 

U 

« 

« 

" 

1.0824 

' 

0.0152 

" 

n 

Strontium     .... 

SrBr2 

1.2901 

' 

0.0186 

«« 

« 

M 

" 

1.1416 

( 

0.0159 

«( 

« 

Carbonate  of  potassium  . 

K2C03 

1.1906 

« 

0.0140 

2O 

" 

"          "  sodium 

Na2C08 

1.  1006 

« 

0.0140 

M 

M 

«                      «                « 

" 

1.0564 

M 

0.0137 

« 

M 

Chlorides  : 

Ammonium  (sal  ammoniac) 

NH4C1 

1.0718 

U 

0.0178 

15 

Verdet. 

Barium 

BaCl2 

1.2897 

H 

0.0168 

20 

Jahn. 

"                       ... 

" 

1-^338 

ft 

0.0149 

u 

" 

Cadmium 

CdCl2 

I-3I79 

" 

0.0185 

" 

4< 

it 

u 

T-2755 

" 

0.0179 

" 

" 

it 

«( 

1.1732 

" 

0.0  1  60 

" 

" 

^6 

-• 

I-I53I 

" 

0.0157 

" 

" 

Calcium 

CaCl2 

1.1504 

" 

0.0165 

M 

<( 

« 

« 

1.0832 

u 

0.0152 

t« 

w 

"                      ... 

« 

1.1049 

" 

0.0157 

16 

Schonrock. 

Copper 

CuCl2 

1.2789 

t< 

0.0221 

o.o  1  86 

15 

Becquerel. 

... 

1-133° 

0.0156 

« 

SMITHSONIAN  TABLES. 


288 


TABLE  3O5, 


MAGNETO-OPTIC    ROTATION. 

Solutions  of  Acids  and  Salts  in  Water. 


Substance. 

Chemical 
formula. 

Density, 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in  minutes. 

Temp. 

Authority. 

Chlorides  : 

Iron      .... 

FeCl2 

M331 

D 

O.OO25 

I5° 

Becquerel. 

"        .         .         . 

" 

1.2141 

" 

0.0099 

1 

" 

« 

" 

1.1093 

" 

0.0118 

• 

u 

" 

« 

1.0548 

" 

0.0124 

1 

tt 

"       (ferric) 

Fe.2Cl6 

1-6933 

« 

—  0.2026 

' 

K 

" 

' 

I-53I5 

" 

—0.1140 

< 

11 

M 

i 

1.3230 

M 

—  0.0348 

< 

" 

H 

< 

1.1681 

<f 

—  0.0015 

' 

" 

" 

< 

1.0864 

* 

0.0081 

' 

<t 

" 

; 

1.0445 

" 

0.0113 

* 

" 

" 

« 

1.0232 

" 

0.0122 

<• 

<( 

Lithium 

LiCl 

1.0619 

«( 

0.0145 

2O 

Jahn. 

"               ... 

M 

1.0316 

M 

0.0143 

tt 

M 

Manganese  . 

MnCl2 

1.1966 

• 

0.0167 

IS 

Becquerel. 

"          ... 

a 

1.0876 

' 

0.0150 

" 

Mercury 

HgCl2 

1.0381 

« 

0.0137 

16 

Schonrock. 

"               ... 

" 

1.0349 

1 

0.0137 

<« 

" 

Nickel. 

NiC)2 

1.4685 

1 

O.O27O 

IS 

Becquerel. 

M 

14 

1.2432 

' 

0.0196 

" 

M 

" 

1.1233 

( 

0.0162 

tt 

<« 

" 

« 

1.0690 

1 

0.0146 

n 

«« 

Potassium    . 

KC1 

i.  6000 

1 

O.OI63 

M 

«< 

"             ... 

i 

1.0732 

1 

0.0148 

20 

Jahn. 

tt 

1 

1.0418 

1 

O.OI44 

<« 

M 

Sodium 

TsaCl 

1.2051 

< 

O.OlSo 

15 

Becquerel. 

tt 

< 

1.1058 

1 

0.0155 

n 

" 

H 

i 

1.0546 

< 

O.OI44 

«< 

<« 

"                          ... 

1 

1.0817 

< 

0.0154 

2O 

Jahn. 

"                         » 

( 

1.0418 

1 

O.OI44 

u 

" 

Strontium     . 

SrCl2 

1.1921 

' 

0.0l62 

It 

«< 

" 

" 

1.0877 

< 

0.0146 

« 

« 

Tin       .         ! 

SnCl2 

1.3280 

' 

O.O266 

15 

Verdet. 

" 

« 

1.1637 

M 

0.0198 

<« 

" 

M 

Zinc      .... 

it 
ZnCl2 

I.III2 
I.285I 

tt 

0.0175 
0.0196 

H 

«< 

H 

u 

M 

I-1S9S 

M 

0.0161 

«« 

« 

Chromate  of  potassium  . 

K2CrO4 

I-3598 

M 

0.0098 

" 

" 

Bichromate  of       " 

K2Cr2O7 

1.0786 

<( 

0.0126 

(t 

" 

Cyanide  of  mercury 

Hy(CN)2 

1.0638 

«( 

0.0136 

16 

Schonrock. 

"         "         " 

" 

1.0425 

« 

0.0134 

H 

" 

«         «         <« 

M 

1.0605 

" 

0.0135 

M 

<« 

Iodides: 

Ammonium  . 

NHJ 

1.5948 

K 

0.0396 

15 

Perkin. 

a 

tt 

1.5688 

" 

0.0386 

M 

it 

« 

1.5109 

" 

0.0358 

" 

(( 

« 

« 

1.2341 

M 

0.0235 

U 

M 

Cadmium     . 

Cdl 

1.5156 

<« 

0.0291 

2O 

Jahn. 

"            ... 

« 

1.2770 

" 

0.0215 

" 

" 

« 

« 

1.1521 

«« 

0.0177 

(I 

« 

Potassium    . 

KI 

1.6743 

« 

0.0338 

15 

Becquerel. 

"             ... 

<« 

I-3398 

M 

0.0237 

" 

"            ... 

H 

1.1705 

M 

0.0182 

II 

" 

"            ... 

" 

1.0871 

" 

0.0152 

tt 

« 

M 

" 

1.2380 

M 

0.02  1  1 

2O 

Jahn. 

"                    ... 

* 

1.1245 

" 

0.0174 

" 

M 

Sodium 

Nal 

i-i939 

" 

O.O2OO 

" 

M 

. 

« 

1.1191 

0.0175 

« 

<« 

SMITHSONIAN   TABLES. 


289 


TABLES  305-307, 


MAGNETO-OPTIC   ROTATION. 

TABLE  305.  —  Solutions  of  Acids  and  Salts  in  Water. 


Substance. 

Chemical 
formula. 

Density, 
grammes 
perc.  c. 

Kind 
of 

light. 

Verdet's 
constant 
in 
minutes. 

Temp. 

Authority. 

Nitrates  : 

Ammonium          . 

NH4NO3 

1.2803 

D 

O.OI2I 

15 

Perkin. 

Potassium    .... 

KNO3 

1.0634 

« 

0.0130 

2O 

Jahn. 

Sodium        .... 

NaNO3 

1.1112 

it 

O.OI3I 

" 

" 

Uranium      .... 

U203.N20S 

2.0267 

a 

0.0053 

M 

Becquerel. 

<( 

" 

1.7640 

" 

0.0078 

" 

u 

« 

* 

L3865 

« 

0.0105 

M 

It 

« 

« 

I.I963 

« 

O.OII5 

u 

u 

Sulphates: 

Ammonium 

(NH4)2S04 

1.2286 

n 

0.0140 

15 

Perkin. 

(acid)        .        . 

NH4.HS04 

I.44I7 

it 

0.0085 

(T 

u 

Barium         .... 

BaSO4 

I.I788 

it 

0.0134 

20 

Jahn. 

« 

a 

1.0938 

tt 

0.0133 

u 

u 

Cadmium     .... 

CdS04 

I.I762 

" 

O.OI39 

tt 

u 

« 

" 

1.0890 

M 

0.0136 

M 

u 

Lithium       . 

Li2SO4 

1.1762 

M 

0.0137 

« 

u 

"              .... 

" 

1.0942 

a 

O.OI35 

It 

U 

Manganese  .... 

MnS04 

I.244I 

u 

0.0138 

a 

It 

"           .... 

M 

1.1416 

ii 

0.0136 

u 

U 

Potassium   .... 

K2SO4 

1-0475 

u 

0.0133 

u 

tt 

Sodium        .... 

NaSO4 

1.066? 

If 

0.0135 

a 

u 

TABLE  306.  -  Solutions  of  Salts  in  Alcohol. 


Substance. 

Chemical 
formula. 

Density, 
grammes 

Kind 
of 

Verdet's 
constant 
in 

Temp. 

Authority. 

per  c.  c. 

light. 

minutes. 

Cadmium  bromide  . 

CdBr2 

1.0446 

D 

0.0159 

20 

Jahn. 

0.9420 

0.0140 

Calcium           "... 

CaBr2 

0.9966 

it 

0.0154 

tt 

< 

a               « 

0.8846 

(t 

0.0130 

Strontium        "        .        .         . 

SrBr2 

0.9636 

u 

O.OI4O 

tt 

< 

U                                  « 

« 

0.8814 

" 

O.OI26 

u 

< 

Cadmium  chloride          ,        . 

CdCl2 

0.8303 

a 

O.OIlS 

it 

c 

Strontium       " 

SrCl2 

0-8313 

u 

O.OIlS 

tt 

< 

«               tt 

«< 

0.8274 

a 

O.OII7 

tt 

< 

Cadmium  iodide              .        ,  ^ 

CdI2 

1.0988 

n 

0.0199 

(i 

1 

<«             « 

u 

0.9484 

U 

0.0156 

H 

TABLE  307.  —  Solutions  in  Hydrochloric  Acid. 


Substance. 

Chemical 
formula. 

Density, 
grammes 
per  c.  c. 

Kind 
of 
light. 

Verdet's 
constant 
in 
minutes. 

Temp. 
C. 

Authority. 

Antimony  trichloride 

SbCl8 

2-4755 

D 

0.0603 

15 

Becquerel. 

4<                   "                       . 

" 

1.8573 

" 

0.0449 

I.5I95 

0.0347 

" 

' 

Bismuth            " 

BiCl8 

1.3420 
2.0822 

0.0277 
0.0396 

« 

< 

" 

1.6550 

n 

0.0359 

" 

1.4156 

0.0350 

SMITHSONIAN  TABLES. 


290 


TABLE  308. 


MAGNETO-OPTIC   ROTATION. 

Gases. 


Verdet's 

Substance. 

Pressure. 

Temp. 

constant  in 

Authority. 

minutes. 

Atmospheric  air 
Carbon  dioxide        .... 

Atmospheric 

Ordinary 

6.83  X  10-6 
13.00 

Becquerel. 

Carbon  disulphide  .... 

74  cms. 

70°  C. 

2349 

Bichat. 

Ethylene           

Atmospheric 

Ordinary 

3448 

Becquerel. 

Nitrogen          

" 

6.92 

" 

Nitrous  oxide  

H 

« 

I6.QO 

« 

Oxygen    

M 

6.28 

H 

Sulphur  dioxide      .... 

(( 

U 

31-39      " 

« 

4(                              « 

246  cms. 

20°  C. 

38.40       " 

Bichat. 

Du  Bois  discusses  Kundt's  results  and  gives  additional  experiments  on  nickel  and  cobalt. 
He  shows  that  in  the  case  of  substances  like  iron,  nickel,  and  cobalt  which  have  a  variable  mag- 
netic susceptibility  the  expression  in  Verdet's  equation,  which  is  constant  for  substances  of  con- 
stant susceptibility,  requires  to  be  divided  by  the  susceptibility  to  obtain  a  constant.  For  this 
expression  he  proposes  the  name  "  Kundt's  constant."  These  experiments  of  Kundt  and  Du 
Bois  show  that  it  is  not  the  difference  of  magnetic  potential  between  the  two  ends  of  the  medium, 
but  the  product  of  the  length  of  the  medium  and  the  induction  per  unit  area,  which  controls  the 
amount  of  rotation  of  the  beam. 


TABLE  309. 


VERDET'S   AND    KUNDT'S   CONSTANTS. 


The  following  short  table  is  quoted  from  Du  Bois'  paper.     The  quantities  are  stated  in  c.  g.  s.  measure,  circular 
measure  (radians)  being  used  in  the  expression  of  "  Verdet's  constant  "  and  "  Kundt's  constant." 


Verdet's  constant. 

Name  of  substance. 

Magnetic 
susceptibility. 

Wave-length 
of  light 
in  cms. 

Kundt's 
constant. 

Number. 

Authority. 

Cobalt      . 

_ 

_ 

_ 

6.44  X  i  o~5 

3-99 

Nickel      . 

— 

— 

— 

4 

3-:5 

Iron 

_ 

— 

— 

6.56 

2.63 

Oxygen  :  i  atmo.     . 
Sulphur  dioxide 

4-o.oi26Xio~5 

—  0.0751 

0.000179  X  io~5 
0.302 

Becquerel. 

« 

5-89 

0.014 
—  4.00 

Water'      . 

—0.0694 

o.377 

Arons 

—5-4 

Nitric  acid 

—0.0633 

0.356 

Becquerel. 

-5.6 

Alcohol    . 

—  0.0566 

0.330 

De  la  Rive. 

-5.8 

Ether  .      . 

—  0.0541 

0-3*5 

" 

-5.8 

Arsenic  chloride 

—  0.0876    " 

1.222                 " 

Becquerel. 

—14.9 

Carbon  disulphide  . 

—  0.0716      " 

1.222                 " 

Rayleigh. 

—17.1 

Faraday's  glass 

—0.0982    " 

1.738 

Becquerel. 

—17.7 

SMITHSONIAN   TABLES. 


2QI 


TABLE  31 0. 

MAGNETIC   SUSCEPTIBILITY    OF    LIQUIDS    AND    CASES. 

The  following  table  gives  a  comparison  by  Du  Bois  *  of  his  own  and  some  other  determinations  of  the  magnetic  sus- 
ceptibility of  a  few  standard  substances.     Verdet's  and  Kundt's  constants  are  in  radians  for  the  sodium  line  D. 


Substance. 

Verdet's 
constant. 

Faraday's 
value 
kX  io« 

Becquerel's 
value 
/5rXio6 

Wahner's 
value 
£Xio<5 

Water   

3.77  X  1C-6 

-0.69 

—  0.63 

—0-536 

Alcohol,  C2H6O   . 

3-30          " 

—0-57 

—0.49 

—0.388 

Ether,  C4Hi0O      .        . 

3-15          " 

—0-54 

- 

—0.360 

Carbon  disulphide 

12.22 

—0.72 

—0.84 

—0.465 

Oxygen  at  I  atmosphere 

O.OOI79  " 

0.13 

O.I2 

- 

Air  at  i  atmosphere 

0.00194  " 

0.024 

0.025 

- 

Substance. 

Quincke  at  20°  C. 

Du  Bois  at  15°  C. 

Density. 

£Xio« 

Density. 

k  XlO<5 

Kundt's 
constant. 

Water   .        .      *. 

0.9983 

—0.815 

0.9992 

-0.837 

—4-5° 

Alcohol,  C2H6O   . 

0.7929 

—0.660 

0.7963 

—0.694 

—4-75 

Ether,  C4H100      . 

0.7152 

—  0.607 

0.7250 

—  0.642 

—4.91 

Carbon  disulphide 

1.2644 

—0.724 

1.2692 

—0.8  1  6 

—14.97 

Oxygen  at  I  atmosphere 

- 

- 

0.00135 

0.117 

0.016 

Air  at  I  atmosphere 

- 

- 

O.OOI23 

0.024 

0.081 

TABLE  311. 


VALUES    OF    KERR'S    CONSTANT.! 


Du  Bois  has  shown  that  the  rotation  of  the  major  axis  of  vibration  of  radiations  normally  reflected  from  a  magnet  is 
algebraically  equal  to  the  normal  component  of  magnetization  multiplied  into  a  constant  K,  He  calls  this  con- 
stant, K,  Kerr's  constant  for  the  magnetized  substance  forming  the  magnet. 


Color  of  light. 

Spectrum 
line. 

Wave- 
length 
in  cms. 
X  10° 

Kerr's  constant  in  minutes  per  c.  g.  s.  unit  of  magnetization. 

Cobalt. 

Nickel. 

Iron. 

Magnetite. 

Red       . 

Li  a 

67.7 

—  O.O2O8 

—0.0173 

—0.0154 

+0.0096 

Red 

— 

62.0 

—  0.0198 

—  0.0160 

—  0.0138 

+O.OI2O 

Yellow  . 

D 

58.9 

—  0.0193 

—  o.oi  54 

—  0.0130 

+0.0133 

Green     . 

b 

51-7 

—  0.0179 

—  0.0159 

—  O.OI  1  1 

+O.OO72 

Blue       . 

F 

48.6 

—  u.olSo 

—  0.0163 

—  o.oi  or 

+  O.OO26 

Violet    . 

G 

43-i 

—  O.Ol82 

—0.0175 

—  0.0089 

- 

*  "  Wied.  Ann."  vol.  35,  p.  163. 
SMITHSONIAN  TABLES. 


t  H.  E.  J.  G.  Du  Bois,  "  Phil. 


vol.  29. 


292 


TABLES  312,  313. 

EFFECT  OF  MAGNETIC  FIELD  ON  THE  ELECTRIC  RE- 
SISTANCE   OF    BISMUTH.* 


TABLE  312.  —  Resistance  One  Ohm  for  Zero  Field  and  Various  Temperatures. 

This  table  gives  the  resistance  to  the  flow  of  a  steady  electric  current  when  conveyed 
across  a  magnetic  field  of  the  strength  in  c.  g.  s.  units  given  in  the  first  column  if 
the  wire  has  a  resistance  of  one  ohm  at  the  temperature  given  at  the  top  of  the  col- 
umn when  the  field  is  of  zero  strength. 


Temp.  C.= 

0° 

10° 

18° 

30° 

60° 

80° 

Field. 

Resistance. 

000 

I.OOO 

I.OOO 

I.OOO 

I.OOO 

.000 

.000 

IOOO 

I.OI8 

1.019 

1.018 

1.017 

.014 

.007 

2OOO 

1.045 

.050 

1.045 

1.041 

.034 

•015 

3OOO 

1.088 

.094 

1.084 

1.074 

•055 

.032 

4OOO 

1-135 

-153 

1.131 

1.118 

.085 

.050 

5°OO 

1.185 

.214 

1.183 

1.156 

•"3 

•074 

6000 

1.240 

•273 

1.242 

i.  202 

.148 

.100 

7OOO 

1.304 

.340 

1.295 

1.258 

.190 

.127 

8000 

1-365 

.406 

1.358 

1.308 

.154 

9OOO 

1.423 

.467 

1.417 

1-355 

.266 

.182 

I  OOOO 

1.480 

•535 

1.480 

1.409 

•3°3 

.203 

1  5000 

1-743 

.875 

1.785 

1.665 

•505 

•343 

2  OOOO 

— 

2.507 

2.087 

1.927 

•713 

1.490 

25000 

- 

2.846 

2-393 

2.193 

I-93I 

1.804 

30000 

— 

—  . 

2.704 

— 

— 

— 

35000 

- 

- 

3-031 

- 

- 

- 

4OOOO 

TABLE  313.  —  Resistance  One  Ohm  for  Zero  Field  and  Temperature  Zero  Cen- 
tigrade. 

This  table  gives  the  resistance  in  different  magnetic  fields  and  at  different  temperatures 
of  a  wire,  the  resistance  of  which  is  one  ohm  at  o°  C.,  when  the  magnetic  field  is 
zero.  The  current  is  supposed  to  be  steady  and  to  flow  across  the  field. 


Temp.  C.= 

0° 

10° 

18° 

30° 

50° 

80° 

Field. 

Resistance.          « 

oooo 

I.OOO 

•037 

1.072 

1.115 

1.200 

1-332 

IOOO 

I.OI8 

.057 

1.091 

1.129 

I.2I7 

I-34I 

2OOO 

1.045 

.089 

1.118 

1.156 

I.24I 

J.352 

3000 

1.  088 

•134 

1.162 

1.198 

1.266 

1-375 

4OOO 

'•135 

.198 

I.2IO 

1.246 

I.3O2 

1-397 

5OOO 

I.l85 

.260 

1.265 

1.290 

1-335 

1.428 

6OOO 

1.240 

•323 

1.327 

I-34I 

1-379 

1.464 

7000 

1.304 

•392 

I-385 

1.404 

1.428 

1.500 

8000 

1.365 

•458 

1-453 

1.460 

1.465 

1-536 

9OOO 
I  OOOO 

1.423 
1.480 

1-523 
1.592 

i-5'5 

1-583 

1.509 
r-573 

1.520 
1.562 

1-573 
1.610 

1  5000 

1-743 

1.946 

1.907 

i.  860 

1.805 

1.784 

2  OOOO 

— 

2.295 

2.243 

2.148 

2-055 

1.980 

25000 

~ 

2.645 

2.560 

2-445 

2.320 

2-157 

*  Calculated  from  the  results  of  J.  B.  Henderson's  experiments,  "  Phil.  Mag."  vol.  38,  p.  488. 
SMITHSONIAN  TABLES. 

293 


TABLE  314. 

SPECIFIC  HEATS  OF  VARIOUS  SOLIDS  AND  LIQUIDS.4 


SOLIDS. 

Substance. 

Temperature 
in 
degrees  C. 

Specific 
heat. 

Authority. 

Alloys  : 

!5~98 

0.0858 

R 

Brass,  redv      .        .     -  .        .        .        .        . 

O 

.08991 

L 

"       yellow  .         .        A"'     ..... 

O 

.08831 

« 

80  Cu  +  20  Sn       .        -«        *        .        *        .*       » 

14-98 

.0862 

R 

88  7  Cu  -f-  ii  3  Al                  

20—  100 

.10432 

Ln 

German  silver         

O-IOO 

.09464 

T 

Lipowitz  alloy  :   24.97  Pb  +  10.13  Cd  +  50.66  Bi 

-f  14.24811          

5-50 

•0345 

M 

ditto        

100-150 

.0426 

u 

Rose's  alloy  :  27.5  Pb  +  48.9  Bi  +  23.6  Sn  . 

—77-20 

.0356 

S 

ditto        ' 

20-89 

.0552 

" 

Wood's  alloy  :  25.85  Pb  +  6.99  Cd  +  52.43  Bi  -f 

14-73  Sn       

5-50 

•0352 

M 

ditto  (fluid)     

100-150 

.0426 

" 

Miscellaneous  alloys  : 

17.5  Sb  +  29.9  Bi  -f  18.7  Zn  -f-  33.9  Sn 

20-99 

.05657 

R 

37.1  Sb  +  62.9  Pb  

10-98 

.03880 

« 

39.9  Pb  -f  6o.iBi  .        .        .'      : 

16-99 

•03165 

P 

ditto  (fluid)     , 

144-358 

.03500 

" 

63.7  Pb  +  36.3  Sn  

12-99 

.04073 

R 

46.7  Pb  4-  53-3  Sn  •        •        •      -  • 
63.8  Bi  4-  36.2  Sn  . 

10-99 
20-99 

.04507 
.04001 

M 

46.961  -j-  53.1  Sn  .        .        .        .        ,        . 

20-99 

.04504 

H 

CdSn2     

—  77—20 

O  C^^7 

« 

Basalt         

/  / 

2O-IOO 

.20-.24 

_ 

Calcspar     «        . 

16-48 

.206 

K 

Diamond   

—  5°"5 

.0635 

H  W 

"           ......... 

10.7 

.1128 

" 

"           ......... 

I4O.O 

.2218 

H 

44           .        .        .        .       '  

206.0 

•2733 

U 

u 

606.7 

.4408 

44 

14 

081; 

It 

Gas  coal     .        .        .        

yu  j 
20-1040 

•3J45 

_ 

Glass,  crown      

10-50 

.161 

HM 

"      flint          .        

10-50 

.117 

" 

"      mirror      

10-50 

.186 

" 

Gneiss        

—  19-20 

.1726 

R  W 

u 

17-213 

.2143 

" 

Granite       

O-IOO 

.I9-.2O 

J&  B 

Graphite    

—50.3 

.1138 

H  W 

"           ......... 

10.8 

.1604 

" 

44           

138.5 

.2542 

M 

"           ......... 

2OI.6 

.2966 

44 

"           ......... 

641.9 

•4450 

M 

tt 

.4.670 

U 

H 

16-1040 

"rw/  w 

.310 

D 

REFERENCES. 

A  M  =  A.  M.  Mayer.                 B  =  Batelli.             D  =  Dewar.                   E  =  Emo. 
G  &  T  =  Gee  &  Terry.              H  &  D  =  De  Keen  &  Deruyts.                   H  M  =  H.  Meyer. 
H  W  =  H.  F.  Weber.               J  &  B  =  Joly  &  Bartoli.                                K  =  Kopp. 
L  =  Lorenz.                      Ln  =  Luginin.                   M  =  Mazotto.                Ma  =  Marignac. 

P  =  Person.                      Pa  =  Pagliani.                  Pn  =  Pionchon.            R  =  Regnault. 

R  W  =  R.  Weber.          T  =  H.  Tomlinson.         Th  =  Thomsen.             W  =  Wachsmuth. 

*  Condensed  from  more  extensive  tables  given  in  Landolt  and  Bornstein's  "  Phys.  Chem.  Tab." 
SMITHSONIAN  TABLES. 

294 


TABLE  314. 


SPECIFIC  HEATS  OF  VARIOUS  SOLIDS  AND  LIQUIDS. 


Substance. 

Temperature 
in 
degrees  C. 

Specific 
heat. 

Authority. 

16-46 
-78-0 
—30-0 
—  21-1 
P-IOO 
16-98 
23-98 

—20-3 

I9-2O 
O-2O 

35-f 
60-63 

0 

350 

400-1200 

17-45 

20-100 

0.259 
.4627 
•5°5 

:i:7 

.2158 
.2099 
.3768 
.5251 
•6939 

.622 

.712 

•m 
$ 

•3312 

K 
R 

P 

G&T 
R 

R  W 

«< 

B 

H 

Pn 

« 

K 
A  M 

Ice      

Marble,  white     •  ,  . 
gray      
Paraffin      

u 

fluid    '.      ! 

Quartz        
Sulphur,  cryst.  ........ 

LIQUIDS. 

—  20 
0 
40 

5-10 
15-10 

10 

40 

o 

15-50 

h 

0 

21-58 
12-15 

12-14 

13-17 

20-52 
20-52 
18 
18 
18 
18 
18 
18 
17-5 
17-5 
17-5 

0-5053 

•5475 
.6479 
.5901 
.6009 
.3402 

•4233 
.5290 

•576 
•434 
•438 
.471 

.387^ 
.4106 

•511 

.848 

•95i 
•975 
.842 

•952 
.876 

•975 
.942 

•983 
.791 
.978 
.980 
•938 
•903 

R 

ii 
11 

u 

H&D 

R 
E 
W 

H  W 

« 

W 
R 

Pa 

« 

« 

Ma 

11 

Th 

11 

« 

« 

11           11 

"         methyl          
Benzene               <         

Ethyl  ether         

"     sesame        
"     turpentine           

CuSO4  -f-  5oH2O              

"       +  200  H2O    
«<       _j_  400  H2O    

ZnSO4  -f  50  HoO      
-f  200  H2O    

KOH    +  30  H2O      
-f  200  H2O    
NaOH+5oH20      . 
+  100  H2O    
NaCl    +  ioH20      
"        4-  200  H2O             

Sea  water  :  density  1.0043         
"         "              "        1-0235  (about  normal) 
"       1-0463          

REFERENCES. 

A  M  =  A.  M.  Maver.                B  =  Batelli.            D  =  Dewar.                  E  =  Emo. 
G  &  T  =  Gee  &  Terry.              H  &  D  =  De  Heen  &  Deruyts.                   H  M  =  H.  Meyer. 
H  W  =  H.  F.  Weber.              J  &  B  =  Joly  &  Bartoli.                              K  =  Kopp. 
L  =  Lorenz.                      Ln  =  Luginin.                   M  =  Mazotto.               Ma  =  Marignac. 
P  =  Person.                      Pa  =  Pagliani.                   Pn  =  Pionchon.           R  =  Regnault. 
R  \V  =  R.  Weber.          T  =  H.  Tomlinson.          Th  =  Thomsen.           W  =  Wachsmuth. 

SMITHSONIAN  TABLES. 


295 


TABLE  315. 


SPECIFIC  HEAT  OF   METALS.^ 


Metal. 

Temperature 
in 

Specific 

•c 

o 

Metal. 

Temperature 
in 

Specific 

1 

degrees  C. 

neat. 

"3 

degrees  C. 

heat. 

1 

Aluminium 

20 

0.2135 

N 

Manganese     .     . 

14-97 

O.I2I7 

R 

"             .     . 

IOO 

.2211 

" 

Mercury  :  solid   . 

—  78  to  —  40 

.03192 

" 

"             .     . 

2OO 

.2306 

" 

"           ... 

20-50 

•033  1  2 

W 

" 

300 

.2401 

" 

u 

0 

•03337 

N 

Antimony  .     .     . 

15 

.04890 

a 

"           ... 

IOO 

.03284 

" 

"          ... 

IOO 

•05031 

u 

it 

2OO 

•03235 

11 

'•    :  :  : 

200 
300 

.05198 
.05366 

u 
u 

Nickel    .     !     '.     ! 

250 
14-97 

.03212 
.10916 

u 

R 

Bismuth     .     .     . 

O 

•03013 

L 

"        .... 

IOO 

.11283 

Pn 

"            ... 

20-84 

•0305 

K 

"        .... 

300 

.14029 

" 

fluid  .     . 

280-380 

•0363 

P 

"        .... 

.12988 

u 

Cadmium  .     .     . 

21 

•0551 

N 

"        .... 

800 

.1484 

" 

u 

IOO 

.0570 

" 

"        .... 

IOOO 

.16075 

" 

"          ... 

200 

•0594 

" 

Palladium  .     .     . 

O-IOO 

.0592 

V 

"            ... 

300 

.0617 

" 

"          ... 

o-i  265 

.0714 

M 

Calcium     .     .     . 

O-IOO 

.1804 

B 

Platinum    .     .     . 

—78-20 

•03037 

S 

Chromium  (?) 

22-51 

•09975 

K 

M 

O-IOO 

•0323 

V 

Cobalt   .... 

9-97 

.10674 

R 

"                    ... 

0-784 

•0365 

M 

"        .... 

500 

.14516 

Pn 

a 

O-I  OOO 

•0377 

M 

"        .... 

IOOO 

.204 

" 

u 

0-1177 

.0388 

U 

Copper  .... 

o 

.08988 

L 

"             ... 

1300 

.03854 

Pt 

M 

5° 

.09166 

" 

"             ... 

1400 

.03896 

" 

"            .... 

17 

.09244 

N 

u 

1600 

.03980 

" 

Ill 

IOO 

ti 

Potassium  .     . 

^,u    -  o  .-> 

T  f^f^'y 

s 

"             .        .        .        . 

2OO 

.09634 

tt 

Silver     .... 

O-IOO 

•°559 

B 

"             .... 

300 

.09846 

" 

"         .... 

23 

.05498 

N 

Gold      .... 

O-IOO 

.0316  „ 

V 

. 

IOO 

.05663 

" 

Iridium      .     .     . 

O-IOO 

•0323 

" 

. 

2OO 

•05877 

" 

"            ... 

0-1400 

.0401 

" 

300 

.06091 

u 

Iron  

15 

.1091 

N 

. 

800 

.076 

Pn 

«     

IOO 

.1151 

M 

fluid     .     . 

907-1100 

.0748 

u 

"     

200 

.1249 

U 

Sodium  .... 

—79-5-17 

.2830 

S 

u 

'JOO 

it 

« 

—  28-6 

2Q^A 

R 

11 

500 

•17645 

Pn 

Tin    .'.'.!! 

—  78-20 

.05416 

S 

a 

•JS}    A    -^  T 

it 

tt 

o 

oc^68 

L 

u 

7  20—  i  ooo 

.218 

tt 

ft 

CO 

!oCC7A 

(l 

IOOO—  I  2OO 

10887 

tt 

n 

J 

75 

'oc6!d  7 

tt 

Lead      .... 

—78-1  1 

.  j.ycj<_>/ 
.03065 

R 

"    fluid    .    .     . 

250-350 

.0637 

P 

"         .... 

15 

•02993 

N 

a      a 

250 

•05799 

Pn 

u 

IOO 

.03108 

it 

"      "        ... 

I  IOO 

.0758 

" 

a 

2OO 

O~*^A4. 

tt 

Zinc  

O-IOO 

OQ7  C 

B 

"     fluid  .     .     . 

-JIO 

Q^ggA 

Sr> 

18 

ooi  t; 

N 

a        it 

O4OQ6 

«f 

< 

iqo 

•oqc.i 

Lithium      .     .     . 

27—  no 

Q4O8 

R 

, 

y 
2OO 

^o 
.oqq6 

u 

Magnesium 

*/   J? 

o 

•yty^>-> 

L 

( 

•  Wl^^Vf 

.104.0 

7  ^ 

'2^00 

'" 

t 

300-400 

•  i  Wif-W 

.122 

LV 

/  j 

REFERENCES. 

B  =  Bunsen.            K  =  Kopp.          L  =  Lorenz.         LV  =  Le  Verrier.         N  =  Naccari. 

P=  Person.              Pn  =  Pionchon.                     Pt  =  Pouillet.                   R  =  Regnault. 

S  =  Schuz.                Sp  =  Spring.                         V  =  Violle.                       W  =  Winkelmann. 

*  Condensed  from  Landolt  and  Bornstein's "  Phys.  Chem.  Tab." 


SMITHSONIAN  TABLES. 


296 


INDEX. 


Absorption  of  gases  by  liquids 125 

of  solar  energy  by  the  atmosphere 177 

Acceleration,  angular  and  linear,  conversion 

factors  for 17,  18 

Activity,  conversion  factors  for 19,  21 

Aerodynamics ;    data    for    the    soaring    of 

planes 109 

data  for  wind  pressure 108 

Agonic  lines 117 

Air,  specific  heat  of 223 

thermometer 228,  229 

Alcohol,  density  of 96-98 

vapor  pressure  of 126,  225 

Alloys,  electric  conductivity  of 251-253 

electric  resistance  of 251-253,  256,  257 

density  of 85 

specific  heat  of 294 

strength  of 73 

thermal  conductivity  of 197 

thermoelectric  power  of 248,  249 

Alternating  currents,  resistance  of  wires  for.  258 

Alums,  indices  of  refraction  for 180 

Angles,  conversion  factors  for 14 

Aqueous  solutions,  boiling-points  of 196 

vapor,  density  of 155 

pressure  of 151—154 

Arc  spectrum,  wave-lengths  in 172 

Areas,  conversion  factors  for 1 1 

Atmosphere,  pressure  of  vapor  in 1 57 

Atomic  weights 272 


Barometer,  correction  for  capillarity 124 

determination  of  heights  by 169 

reduction  to  latitude  45° 122',  123 

reduction  to  sea  level 121 

reduction  to  standard  temperature 120 

Battery  cells,  composition  and  electromotive 

force  of 246,  247 

Bismuth,  electric  resistance  of,  in  magnetic 

field 293 

Boiling-point,  of  chemical  elements 207 

of  various  inorganic  compounds 210 

of  various  organic  compounds 212 

of  water,  barometric  height  correspond- 
ing to 171 

of  water,  effect  of  dissolved  salts  on 196 

Brick,  strength  of 70 

British  weights  and  measures,  equivalents  in 
metric 7 


Capacities,  conversion  factors  for 12 

Capacity,  specific  inductive 263-265 

Capillarity,  of  aqueous  solutions 128 

correction  of  barometer  for 124 

of  liquids  as  solidifying-point 129 

of  soap  films 1 29 


Capillarity  (continued}. 

surface-tension  of  water  and  alcohol  ...  128 

various  liquids 1 27 

Carat,  definition  of 18 

Cells,  battery 246,  247 

secondary 247 

standard 247 

Chemical    elements,    boiling     and    melting 

points  of 207 

Cobalt,  Kerr's  constants  of 291 

magnetic  properties  of 279 

Coefficients,  isotonic 150 

of  diffusion 147,  149 

of  friction 135 

of  thermal  expansion 314-218 

of  viscosity 137,  146 

Color    scale,    Newton    and    Reinold    and 

Rucker 130 

Combination,  heat  of 202 

Combustion,  heat  of    201 

Compressibility,  of  gases 79,  81 

of  liquids 82 

of  solids 83 

Conducting  power  of  alloys 251-253 

Conductivities,  molecular 260,  261 

of  electrolytes 259 

thermal 197,  198 

Contact,  difference  of  potential 268 

Conversion  factor,  definition  of xviii 

Conversion  factors  for  acceleration,  angular . .  18 

acceleration,  linear 17 

activity 19,  21 

angles 14 

areas  . .  . .  1 1 


capacities 

densities    

electric  deposition 

electric  displacement 

electric  potential 

electric  resistance 

energy 20, 

film  tension 20, 

force  

heat,  quantities  of 

intensity  of  magnetization 

length 

masses 

moment  of  inertia 

moment  of  momentum 

momentum  . 


magnetic  moment 

magnetization,  intensity  of 

magnetization,  surface  density  of 

power 19, 

resistance,  electric 

stress 19, 

temperatures 

tension,  film  or  surface 


298 


INDEX. 


Conversion  (continued). 

time,  intervals  of 14 

velocities 15 

volumes 12 

work 20,  2 1 

Critical  temperature  of  gases 200 

Crystals,  cubic  expansion  of 216 

elastic  constants  of 78 

formulae  for  elasticity  of 77 

refractive  indices  of 187 

Cubic  expansion,  gases 218 

liquids 217 

solids 216 

Cyclic  magnetization,  dissipation  of  energy 
in 280-283 


Declination,  magnetic 1 13-118 

Densities,  of  air,  values  of  h/i&> 162 

alcohol 96-98 

alloys  and  other  solids 85 

aqueous  solutions 90 

gases 89 

liquids 88 

mercury 95 

metals 86 

organic  compounds 212 

water 92-94 

woods 87 

Density,  conversion  factors  for 23 

Dew-points,  table  for  calculating 158 

Diamonds,  unit  of  weight  for 13 

Dielectric  strength 244,  245 

Diffusion  of  gases  and  vapors 149 

liquids  and  solutions 147 

Dilution  of  solution,  contraction  due  to  ....  134 

Dimension  formulas  (see  also  Units] xvii 

Dip,  magnetic 1 1 1 

Dynamic  units,  dimension  formulae  of xvii 

formulae  for  conversion  of 2 

Dynamical  equivalent  of  thermal  unit 219 


Earth,  miscellaneous  data  concerning 106 

Elasticity,  moduli  of 7  4-78 

Electric  conductivity  of  alloys 251,  252 

of  metals 255 

relation  to  thermal 271 

constants  of  wires 58-68,  254 

displacement 25 

potential,  conversion  factors  for 27 

resistance,  conversion  factors  for 23 

resistance,  effect  of  elongation  on 258 

units,  conversion  factors  for 3 

units,  dimension  formulae xxv 

Electrochemical     equivalents     and     atomic 

weights 272 

of  solutions 259 

Electrolytes,  conductivities  of 259 

Electrolytic  deposition,  conversion  factors  for .  24 

Electromagnetic  system  of  units xxix 

Electromotive  force  of  battery  cells 246,  247 

Electrostatic  system  of  units xxvi 

Electrostatic  unit  of  electricity,  ratio  of,  to 

electromagnetic 243 

Elliptic  integrals 43 

P^longation,  effect  on  resistance  of  wires 258 

Emissivity 234,  235 

Energy,  conversion  factors  for 20,  21 

Equivalent,  electrochemical 272 

electrochemical  of  solutions 259 

mechanical,  of  heat 220 

Expansion,  thermal 214,  218 


Factors,  conversion 1 1  -27 

formulae  for  conversion 2,  3 

Film-tension,  conversion  factors  for 20,  22 

constants  for 1 28,  1 29 

Fluor  spar,  refractive  index  of 183 

Formulae   for   conversion    factors,   dynamic 

units 2 

electric  and  magnetic  units 3 

fundamental  units 2 

geometric  units 2 

heat  units ' 3 

Formulae,  dimension  (see  also  Units],  .xvii-xxix 

Force,  conversion  factors  for 17 

Force  de  cheval,  definition  of 19 

Fraunhofer  lines,  wave-lengths  of 175 

Freezing  mixtures 199 

Freezing-point,  lowering  of,  by  salts 192 

Friction,  coefficients  of 135 

Functions,  hyperbolic 28~35 

gamma 38 

Fundamental  units 2 

Fusion,  latent  heat  of 206 


Gamma  functions 38 

Gases,  absorption  by  liquids 125 

compressibility  of 79~8i 

critical  temperatures  of 200 

density  and  specific  gravity  of .89 

expansion  of 218 

magnetic  susceptibility  of . .    292 

magneto-optic  rotation  in 291 

refractive  indices  of 190 

specific  heat  of 224 

thermal  conductivity  of 198 

viscosity  of 145, 146 

volume  of  perfect  (values  of  i  -f-  .00367  /) 

164-168 

Gauges,  wire 58-68 

Geometric  units,  conversion  formulae  for 2 

Glass,  electric  resistance  of 270 

indices  of  refraction  for 178,  179 

Gravity,  force  of 102-104 


Harmonics,  zonal 40 

Heat,  conversion  factors  for  quantities  of. . .  .24 

latent  heat  of  fusion 206 

latent  heat  of  vaporization 204 

mechanical  equivalent  of 220 

units,  conversion  factors  for 24 

dimension  formulae  for xxiii 

formulae  for  conversion  factors  of . . .  .3 
Heats  of  combustion  and  combination. .  201,  202 

Heights,  determination  by  barometer 169 

Humidity,  relative 161 

Hydrogen  thermometer  233 

Hyperbolic  cosines 29-31 

Hyperbolic  functions 28-3 5 

Hyperbolic  sines 28-30 

Hysteresis,  magnetic 280-283 


Iceland  spar,  refractive  index  of 185 

Indices  of  refraction  for  alums 180 

crystals 187 

fluor  spar 185 

gases  and  vapors 190 

glass 178,  179 

Iceland  spar 185 

liquids,  various 189 

metals  and  metallic  oxides 181 

monorefringent  solids  ...    184 


INDEX. 


299 


Indices  of  refraction  for  alums  (continued). 

quartz 186 

rock  salt 182 

solutions  of  salts 188 

sylvine 182 

Inductance,  mutual 42 

Integrals,  elliptic 43 

Intensity,  horizontal,  of  earth's  magnetic  field 

112 

total,  of  earth's  magnetic  field no 

Iron,  elasticity  and  strength  of 72 

hysteresis  in 280-283 

magnetic  properties  of 274-283,  292 

Isotonic  coefficients 150 


Jewels,  unit  of  weight  for 13 

Joule's  equivalent 220 


Kerr's  constant,  definition  and  table  of. . . .  .292 

Kilogramme,  definition  of xvi 

Kundt's  constants 291 

definition  of 291 


Latent  heat 204,  206 

Least  squares,  various  tables  for 35,  37 

Legalization  of  practical  electric  units xxxiv 

Length,  conversion  factors  for 1 1 

Light,  velocity  of 176-243 

rotation  of  plane  of  polarized 191 

Linear  expansion  of  chemical  elements 214 

of  various  substances 215 

Liquids,  absorption  of  gases  by 125 

compressibility  and  bulk  moduli  of 82 

density  of 88 

magneto-optic  rotation  in 286,  287 

magnetic  susceptibility 292 

refractive  indices  of 189 

specific  heat  of 295 

thermal  conductivity  of 197,  198 

thermal  expansion  of 217 

Lowering  of  freezing-point  by  salts 192 


Magnetic  field,  effect  of,  in  resistance  of  bis- 
muth   293 

moment,  conversion  factors  for 27 

permeability 274-280 

properties   of   cobalt,  manganese  steel, 

magnetite  and  nickel 279 

properties  of  iron  and  steel 276 

saturation  values  for  steel 279 

susceptibility  of  liquids  and  gases 292 

units,  conversion  formulae  for 3 

dimension  formulae  for xxv 

Magnetism,  conversion  factors  for  surface 

density 26 

terrestrial 4 1 10-1 18 

Magnetization,  conversion  factors  for  inten- 
sity of 26 

Magnetite,  Kerr's  constant  for 292 

magnetic  properties  of 279 

Magneto-optic  rotation,  general  reference  to 

284 

tables  of 285-291 

Masses,  conversion  factors  for 13 

Materials,  strength  of 7°~73 

Measurement,  units  of xv 

Mechanical  equivalent  of  heat 220 

Melting-points  of  chemical  elements 207 

of  inorganic  compounds 208 


Melting-points  (continued}. 

of  mixtures  and  alloys 211 

of  organic  compounds 212 

Mercury,  density  of 86 

electric  resistance  of 255,  256 

index  of  refraction 181 

specific  heat  of 225 

strength  of 70 

Metals,  density  of 86 

electric  resistance  of 254-258 

specific  heat  of 296 

thermal  conductivity  of 197 

Metals  and  metallic  oxides,  indices  of  refrac- 
tion for 181 

Metre,  definition  of xvi 

Metric  weights  and  measures  — 

equivalents  in  British 5 

equivalents  in  United  States 10 

Mixtures,  freezing 199 

Moduli  of  elasticity 74-83 

Molecular  conductivities 261,  262 

Moments  of  inertia,  conversion  factors  for. . .  13 
Moment   of   momentum,   conversion   factor 

for 16 

Momentum,  conversion  factors  for 13 

Mutual  inductance,  table  for  calculating 42 


Neutral-points,  thermoelectric 249 

Newton's  rings  and  scale  of  colors 130 

Nickel,  Kerr's  constants  for 292 

magnetic  properties  of 279 


Ohm,  various  determinations  of 262 

Osmose  and  osmotic  pressure 150 


Pearls,  unit  of  weight  for 13 

Peltier  effect 250 

Pendulum,  length  of  seconds 104,  105 

Permeability,  magnetic 274-280 

Photometric  standards 176 

Planets,  miscellaneous  data  concerning 106 

Poisson's  .ratio 76 

Polarized  light,  rotation  of  the  plane  of  ....  191 

Potential,  contact  difference  of .-.  .  .268 

difference  of,  between  metals  in  solu- 
tions   269 

electric,  conversion  factors  for 27 

Pound,  definition  of xvi 

Power,  conversion  factors  for 19,  21 

Practical  electrical  units xxxiii 

Pressure,  barometric,  for   different   boiling- 
points  of  water 1 70,  171 

critical,  of  gases 200 

effect  on  radiation 236 

of  aqueous  vapor 1 51-1 54 

at  low  temperatures 1 56 

in  the  atmosphere 1 57 

of  mercury  column 119 

osmotic 150 

of  vapors 126,  225-227 

of  wind 1 08 

Probability,  table  for  calculating 36 


Quartz,  fibres,  strength  of 70 

refractive  index  of . .  186 


Radiation,  effect  of  pressure  on 236 

Relative  humiditv 161 


300 


INDEX. 


Resistance  (see  also  Condiictivity],  electric. 

of  alloys 251-253,  256,  257 

of  electrolytes 259 

of  glass  and  porcelain 270 

of  metals  and  metallic  wires 254-257 

of  wires,  effect  of  elongation  on .258 

Rigidity,  modulus  defined 74 

of  metals 74 

variation  of,  with  temperature 76 

Rotation,  magneto-optic 284-291 


Saturation  values,  magnetic,  for  steel 279 

Seconds  pendulum,  length  of 104,  105 

Secondary  batteries 247 

Sections  of  wires 44~54»  58-68 

Sheet  metal,  weight  of 56,  57 

Soaring  of  planes,  data  for. 109 

Solar  constant 177 

Solar  spectrum,  wave-length  in 172 

Solids,  compressibility  and  bulk  moduli  of . .  .83 

density  of 85 

magneto-optic  rotation  in 284 

Solution,  contraction  produced  by 131-134 

Solutions,  aqueous,  boiling-points  of 196 

density  of 90 

magneto-optic  rotation  in 288-290 

refractive  indices  for 188 

specific  heat  of 224 

Sound,  velocity  of,  in  air 99 

in  gases  and  liquids 101 

in  solids 100 

Specific  electrical  resistance,  conversion  fac- 
tors for 23,  254-256 

Specific  gravity  (see  also  Density}. 

of  aqueous  ethyl  alcohol 96 

methyl  alcohol 97 

of  gases 89 

Specific  heat  of  air 223 

of  gases  and  vapors 224 

of  metals 296 

of  solids  and  liquids 294,  295 

of  water. . .  .^ 223 

of  water,  formulae  for 222 

Specific  inductive  capacity 263-265 

viscosity,  aqueous  solutions 144 

oils 137 

water 136 

Spectra,  wave-lengths  in  arc  and  solar 172 

Standard  cells 247 

wave-lengths  of  light 172 

Standards,  photometric 176 

Steel,  physical  properties  of 71 

Steam,  properties  of  saturated 237 

Steinmetz,  constants  for  hysteresis  of 281 

Stone,  strength  of 70 

thermal  conductivity  of 197 

dielectric 244 

Strength  of  materials 7°~73 

Stress,  conversion  factors  for 19,  22 

Surface-tension,  constants  of 128,  129 

conversion  factors  for 20,  22 

Sylvine,  refractive  index  of 182 


Temperature,  conversion  factors  for 25 

critical,  of  gases 200 

Terrestrial  magnetism,  agonic  lines 117 

declination,  data  for  maximum  east  at 

various  stations 1 18 

dip  and  its  secular  variation  for  differ- 
ent latitudes  and  longitudes in 


Terrestrial  magnetism  (continued). 

horizontal  intensity  and  its  secular  varia- 
tion for  different  latitudes  and  longi- 
tudes   112 

secular  variation  of  declination 1 13-1 16 

Thermal  conductivities 197,  198 

relation  to  electrical 271 

expansion,  coefficients  of 214-218 

units,  dynamic  equivalent  of 219 

Thermoelectricity 248-250 

Thermometer 228-233 

air .228,  231 

correction  of,  for  mercury  in  stem 232 

hydrogen 231 

mercury  in  glass 229 

zero  change  due  to  heating 229 

zero,  change  of,  with  time 230 

Timber,  strength  of 70 

Time,  unit  of,  defined .xvii 

Times,  conversion  factors  for 14 

Transformers,  permeability  of 
iron  in 274,  275,  280,  282 

Units  of  measurement xv 

dimension  formulae  for  dynamic xviii 

electric  and  magnetic xxv 

electromagnetic xxix 

electrostatic xxvi 

fundamental 2 

heat xxiii 

practical,  legalization  of  electric xxxiii 

ratio  of  electrostatic  to  electromagnetic 

243 

United    States    weights    and    measures    in 
metric 9 


Vapor,  density  of  aqueous 155 

diffusion  of 1 49 

pressure  of 126,  225-227 

pressure  of  aqueous 151-154 

values  of  0.378*? 160 

pressure  of,  for  aqueous  solutions 194 

refractive  indices  for .' 190 

specific  heats  of 224 

Vaporization,  latent  heat  of 204 

Velocity,  angular  and  linear,  conversion  fac- 
tors for 15 

of  light 176,  243 

of  sound 99,  101 

Verdet's  constants  for  alcoholic  solution  of 

salts 290 

aqueous  solutions  of  salts 287 

gases 291 

hydrochloric  acid  solutions  of  salts  290 

liquids  and  solids 285-287 

and  Kundt's  constants 292 

Viscosity,  coefficient,  definition  of 136 

coefficient  of,  for  aqueous  alcohol 137 

for  gases 146 

for  liquids 138 

temperature  effect  on,  for  liquids 139 

specific,  for  oils 137 

for  water 136 

Volumes,  conversion  ftifors  for 12 

critical,  of  gases 200 


Water,  boiling-point  for  various  barometric 

pressures 170,  171 

density  of 92-94 

specific  heat  of 222,  223 


7  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 


This  publication  is  due  on  the  LAST  DATE 
stamped  below. 


General  Library 

University  of  Californi 

Berkeley 


RB  17-60m-8,'60 
(B3395slO)4188 


810844 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


• 


